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-rw-r--r--Content/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.md55
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-rw-r--r--docs/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html10
-rw-r--r--docs/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html90
-rw-r--r--docs/posts/index.html11
-rw-r--r--docs/tags/mathematics.html11
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diff --git a/Content/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.md b/Content/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.md
new file mode 100644
index 0000000..0435a6c
--- /dev/null
+++ b/Content/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.md
@@ -0,0 +1,55 @@
+---
+date: 2024-03-26 15:36
+description: Quick derivation of the quadratic equation by completing the square
+tags: mathematics
+---
+
+# Quadratic Formula Derivation
+
+The standard form of a quadratic equation is:
+
+$$
+ax^2 + bx + c = 0
+$$
+
+Here, $a, b, c \in \mathbb{R}$, and $a \neq 0$
+
+We begin by first dividing both sides by the coefficient $a$
+
+$$
+\implies x^2 + \frac{b}{a}x + \frac{c}{a} = 0
+$$
+
+We can rearrange the equation:
+
+$$
+x^2 + \frac{b}{a}x = - \frac{c}{a}
+$$
+
+We can then use the method of completing the square. ([Maths is Fun](https://www.mathsisfun.com/algebra/completing-square.html) has a really good explanation for this technique)
+
+$$
+x^2 + \frac{b}{a}x + (\frac{b}{2a})^2 = \frac{-c}{a} + (\frac{b}{2a})^2
+$$
+
+On our LHS, we can clearly recognize that it is the expanded form of $(x + d)^2$ i.e $x^2 + 2x\cdot d + d^2$
+
+$$
+\implies (x + \frac{b}{2a})^2 = \frac{-c}{a} + \frac{b^2}{4a^2} = \frac{-4ac + b^2}{4a^2}
+$$
+
+Taking the square root of both sides
+
+$$
+\begin{align*}
+x + \frac{b}{2a} &= \frac{\sqrt{-4ac + b^2}}{2a} \\
+x &= \frac{\pm \sqrt{-4ac + b^2} - b}{2a} \\
+&= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
+\end{align*}
+$$
+
+This gives you the world famous quadratic formula:
+
+$$
+x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
+$$
diff --git a/Resources/images/opengraph/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.png b/Resources/images/opengraph/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.png
new file mode 100644
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--- /dev/null
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diff --git a/docs/feed.rss b/docs/feed.rss
index 12e9f8d..12b90df 100644
--- a/docs/feed.rss
+++ b/docs/feed.rss
@@ -4,8 +4,8 @@
<title>Navan's Archive</title>
<description>Rare Tips, Tricks and Posts</description>
<link>https://web.navan.dev/</link><language>en</language>
- <lastBuildDate>Thu, 21 Mar 2024 14:27:28 -0000</lastBuildDate>
- <pubDate>Thu, 21 Mar 2024 14:27:28 -0000</pubDate>
+ <lastBuildDate>Tue, 26 Mar 2024 18:20:37 -0000</lastBuildDate>
+ <pubDate>Tue, 26 Mar 2024 18:20:37 -0000</pubDate>
<ttl>250</ttl>
<atom:link href="https://web.navan.dev/feed.rss" rel="self" type="application/rss+xml"/>
@@ -557,9 +557,7 @@ creating<span class="w"> </span>a<span class="w"> </span>DOS<span class="w"> </s
<script src="https://cdn.jsdelivr.net/npm/mathjax@4.0.0-beta.4/input/tex/extensions/noerrors.js" charset="UTF-8"></script>
-<p>$$
-y = ax^3 + bx^2 + cx + d
-$$</p>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>y</mi><mo>&#x0003D;</mo><mi>a</mi><msup><mi>x</mi><mn>3</mn></msup><mo>&#x0002B;</mo><mi>b</mi><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mi>c</mi><mi>x</mi><mo>&#x0002B;</mo><mi>d</mi></mrow></math>
<h3>Optimizer Selection &amp; Training</h3>
@@ -584,9 +582,7 @@ $$</p>
<p>Our loss function is Mean Squared Error (MSE):</p>
-<p>$$
-= \frac{1}{n} \sum_{i=1}^{n}{(Y_i - \hat{Y_i})^2}
-$$</p>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>&#x0003D;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><msubsup><mo>&#x02211;</mo><mrow><mi>i</mi><mo>&#x0003D;</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><mo stretchy="false">&#x00028;</mo><mi>Y</mi><mi>&#x0005F;</mi><mi>i</mi><mo>&#x02212;</mo><mover><mrow><mi>Y</mi><mi>&#x0005F;</mi><mi>i</mi></mrow><mo stretchy="false">&#x0005E;</mo></mover><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup></mrow></mrow></math>
<p>Where <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false" style="math-style:normal;math-depth:0;">^</mo></mover></math> is the predicted value and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Y</mi><mi>i</mi></msub></math> is the actual value</p>
@@ -726,7 +722,7 @@ $$</p>
<p>How would you modify this code to use another type of nonlinear regression? Say, </p>
-<p>$$ y = ab^x $$</p>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>y</mi><mo>&#x0003D;</mo><mi>a</mi><msup><mi>b</mi><mi>x</mi></msup></mrow></math>
<p>Hint: Your loss calculation would be similar to:</p>
@@ -3188,6 +3184,52 @@ values using the X values. We then plot it to compare the actual data and predic
<item>
<guid isPermaLink="true">
+ https://web.navan.dev/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html
+ </guid>
+ <title>
+ Quadratic Formula Derivation
+ </title>
+ <description>
+ Quick derivation of the quadratic equation by completing the square
+ </description>
+ <link>https://web.navan.dev/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html</link>
+ <pubDate>Tue, 26 Mar 2024 15:36:00 -0000</pubDate>
+ <content:encoded><![CDATA[<h1>Quadratic Formula Derivation</h1>
+
+<p>The standard form of a quadratic equation is:</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mi>b</mi><mi>x</mi><mo>&#x0002B;</mo><mi>c</mi><mo>&#x0003D;</mo><mn>0</mn></mrow></math>
+
+<p>Here, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>&#x0002C;</mo><mi>b</mi><mo>&#x0002C;</mo><mi>c</mi><mo>&#x02208;</mo><mi>&#x0211D;</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>&#x02260;</mo><mn>0</mn></mrow></math></p>
+
+<p>We begin by first dividing both sides by the coefficient <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi></mrow></math></p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>&#x027F9;</mi><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mi>x</mi><mo>&#x0002B;</mo><mfrac><mrow><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mo>&#x0003D;</mo><mn>0</mn></mrow></math>
+
+<p>We can rearrange the equation:</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mi>x</mi><mo>&#x0003D;</mo><mo>&#x02212;</mo><mfrac><mrow><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac></mrow></math>
+
+<p>We can then use the method of completing the square. (<a rel="noopener" target="_blank" href="https://www.mathsisfun.com/algebra/completing-square.html">Maths is Fun</a> has a really good explanation for this technique)</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mi>x</mi><mo>&#x0002B;</mo><mo stretchy="false">&#x00028;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mo>&#x0002B;</mo><mo stretchy="false">&#x00028;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup></mrow></math>
+
+<p>On our LHS, we can clearly recognize that it is the expanded form of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">&#x00028;</mo><mi>x</mi><mo>&#x0002B;</mo><mi>d</mi><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup></mrow></math> i.e <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mn>2</mn><mi>x</mi><mi>&#x000B7;</mi><mi>d</mi><mo>&#x0002B;</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></math></p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>&#x027F9;</mi><mo stretchy="false">&#x00028;</mo><mi>x</mi><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mo>&#x0002B;</mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi><mo>&#x0002B;</mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow></math>
+
+<p>Taking the square root of both sides</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable displaystyle="true" rowspacing="3pt" columnspacing="0em 2em"><mtr><mtd columnalign="right"><mi>x</mi><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mtd><mtd columnalign="left"><mi /><mo>&#x0003D;</mo><mfrac><mrow><msqrt><mrow><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi><mo>&#x0002B;</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd columnalign="right"><mi>x</mi></mtd><mtd columnalign="left"><mi /><mo>&#x0003D;</mo><mfrac><mrow><mi>&#x000B1;</mi><msqrt><mrow><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi><mo>&#x0002B;</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt><mo>&#x02212;</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd columnalign="right" /><mtd columnalign="left"><mi /><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mi>b</mi><mi>&#x000B1;</mi><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mtd></mtr></mtable></mrow></math>
+
+<p>This gives you the world famous quadratic formula:</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>x</mi><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mi>b</mi><mi>&#x000B1;</mi><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow></math>
+]]></content:encoded>
+ </item>
+
+ <item>
+ <guid isPermaLink="true">
https://web.navan.dev/posts/2022-08-05-Why-You-No-Host.html
</guid>
<title>
diff --git a/docs/images/opengraph/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.png b/docs/images/opengraph/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.png
new file mode 100644
index 0000000..2464364
--- /dev/null
+++ b/docs/images/opengraph/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.png
Binary files differ
diff --git a/docs/index.html b/docs/index.html
index 0a3070a..c462f4b 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -50,6 +50,17 @@
<h2>Recent Posts</h2>
<ul>
+ <li><a href="/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html">Quadratic Formula Derivation</a></li>
+ <ul>
+ <li>Quick derivation of the quadratic equation by completing the square</li>
+ <li>Published On: 2024-03-26 15:36</li>
+ <li>Tags:
+
+ <a href='/tags/mathematics.html'>mathematics</a>
+
+ </ul>
+
+
<li><a href="/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html">Polynomial Regression Using TensorFlow 2.x</a></li>
<ul>
<li>Predicting n-th degree polynomials using TensorFlow 2.x</li>
@@ -106,19 +117,6 @@
</ul>
- <li><a href="/posts/2024-01-05-hello-20224.html">Hello 2024</a></li>
- <ul>
- <li>Recap of 2023, and my goals for 2024</li>
- <li>Published On: 2024-01-05 23:16</li>
- <li>Tags:
-
- <a href='/tags/General.html'>General</a>,
-
- <a href='/tags/Ramblings.html'>Ramblings</a>
-
- </ul>
-
-
</ul>
<b>For all posts go to <a href="/posts">Posts</a></b>
diff --git a/docs/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html b/docs/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html
index 7a25daf..ab46ec7 100644
--- a/docs/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html
+++ b/docs/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html
@@ -107,9 +107,7 @@
<script src="https://cdn.jsdelivr.net/npm/mathjax@4.0.0-beta.4/input/tex/extensions/noerrors.js" charset="UTF-8"></script>
-<p>$$
-y = ax^3 + bx^2 + cx + d
-$$</p>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>y</mi><mo>&#x0003D;</mo><mi>a</mi><msup><mi>x</mi><mn>3</mn></msup><mo>&#x0002B;</mo><mi>b</mi><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mi>c</mi><mi>x</mi><mo>&#x0002B;</mo><mi>d</mi></mrow></math>
<h3>Optimizer Selection &amp; Training</h3>
@@ -134,9 +132,7 @@ $$</p>
<p>Our loss function is Mean Squared Error (MSE):</p>
-<p>$$
-= \frac{1}{n} \sum_{i=1}^{n}{(Y_i - \hat{Y_i})^2}
-$$</p>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>&#x0003D;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><msubsup><mo>&#x02211;</mo><mrow><mi>i</mi><mo>&#x0003D;</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><mo stretchy="false">&#x00028;</mo><mi>Y</mi><mi>&#x0005F;</mi><mi>i</mi><mo>&#x02212;</mo><mover><mrow><mi>Y</mi><mi>&#x0005F;</mi><mi>i</mi></mrow><mo stretchy="false">&#x0005E;</mo></mover><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup></mrow></mrow></math>
<p>Where <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false" style="math-style:normal;math-depth:0;">^</mo></mover></math> is the predicted value and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Y</mi><mi>i</mi></msub></math> is the actual value</p>
@@ -276,7 +272,7 @@ $$</p>
<p>How would you modify this code to use another type of nonlinear regression? Say, </p>
-<p>$$ y = ab^x $$</p>
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>y</mi><mo>&#x0003D;</mo><mi>a</mi><msup><mi>b</mi><mi>x</mi></msup></mrow></math>
<p>Hint: Your loss calculation would be similar to:</p>
diff --git a/docs/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html b/docs/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html
new file mode 100644
index 0000000..6f02f7c
--- /dev/null
+++ b/docs/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html
@@ -0,0 +1,90 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
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+ <title>Quadratic Formula Derivation</title>
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+ <h1>Quadratic Formula Derivation</h1>
+
+<p>The standard form of a quadratic equation is:</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mi>b</mi><mi>x</mi><mo>&#x0002B;</mo><mi>c</mi><mo>&#x0003D;</mo><mn>0</mn></mrow></math>
+
+<p>Here, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>&#x0002C;</mo><mi>b</mi><mo>&#x0002C;</mo><mi>c</mi><mo>&#x02208;</mo><mi>&#x0211D;</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>&#x02260;</mo><mn>0</mn></mrow></math></p>
+
+<p>We begin by first dividing both sides by the coefficient <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi></mrow></math></p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>&#x027F9;</mi><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mi>x</mi><mo>&#x0002B;</mo><mfrac><mrow><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mo>&#x0003D;</mo><mn>0</mn></mrow></math>
+
+<p>We can rearrange the equation:</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mi>x</mi><mo>&#x0003D;</mo><mo>&#x02212;</mo><mfrac><mrow><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac></mrow></math>
+
+<p>We can then use the method of completing the square. (<a rel="noopener" target="_blank" href="https://www.mathsisfun.com/algebra/completing-square.html">Maths is Fun</a> has a really good explanation for this technique)</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mi>x</mi><mo>&#x0002B;</mo><mo stretchy="false">&#x00028;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mo>&#x0002B;</mo><mo stretchy="false">&#x00028;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup></mrow></math>
+
+<p>On our LHS, we can clearly recognize that it is the expanded form of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">&#x00028;</mo><mi>x</mi><mo>&#x0002B;</mo><mi>d</mi><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup></mrow></math> i.e <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>&#x0002B;</mo><mn>2</mn><mi>x</mi><mi>&#x000B7;</mi><mi>d</mi><mo>&#x0002B;</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></math></p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>&#x027F9;</mi><mo stretchy="false">&#x00028;</mo><mi>x</mi><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><msup><mo stretchy="false">&#x00029;</mo><mn>2</mn></msup><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mi>c</mi></mrow><mrow><mi>a</mi></mrow></mfrac><mo>&#x0002B;</mo><mfrac><mrow><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi><mo>&#x0002B;</mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac></mrow></math>
+
+<p>Taking the square root of both sides</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable displaystyle="true" rowspacing="3pt" columnspacing="0em 2em"><mtr><mtd columnalign="right"><mi>x</mi><mo>&#x0002B;</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mtd><mtd columnalign="left"><mi /><mo>&#x0003D;</mo><mfrac><mrow><msqrt><mrow><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi><mo>&#x0002B;</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd columnalign="right"><mi>x</mi></mtd><mtd columnalign="left"><mi /><mo>&#x0003D;</mo><mfrac><mrow><mi>&#x000B1;</mi><msqrt><mrow><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi><mo>&#x0002B;</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt><mo>&#x02212;</mo><mi>b</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd columnalign="right" /><mtd columnalign="left"><mi /><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mi>b</mi><mi>&#x000B1;</mi><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mtd></mtr></mtable></mrow></math>
+
+<p>This gives you the world famous quadratic formula:</p>
+
+<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>x</mi><mo>&#x0003D;</mo><mfrac><mrow><mo>&#x02212;</mo><mi>b</mi><mi>&#x000B1;</mi><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>&#x02212;</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow></math>
+
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diff --git a/docs/posts/index.html b/docs/posts/index.html
index d886b19..40b6a92 100644
--- a/docs/posts/index.html
+++ b/docs/posts/index.html
@@ -52,6 +52,17 @@
<ul>
+ <li><a href="/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html">Quadratic Formula Derivation</a></li>
+ <ul>
+ <li>Quick derivation of the quadratic equation by completing the square</li>
+ <li>Published On: 2024-03-26 15:36</li>
+ <li>Tags:
+
+ <a href='/tags/mathematics.html'>mathematics</a>
+
+ </ul>
+
+
<li><a href="/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html">Polynomial Regression Using TensorFlow 2.x</a></li>
<ul>
<li>Predicting n-th degree polynomials using TensorFlow 2.x</li>
diff --git a/docs/tags/mathematics.html b/docs/tags/mathematics.html
index b948423..eb5201c 100644
--- a/docs/tags/mathematics.html
+++ b/docs/tags/mathematics.html
@@ -49,6 +49,17 @@
<ul>
+ <li><a href="/posts/2024-03-26-Derivation-of-the-Quadratic-Equation.html">Quadratic Formula Derivation</a></li>
+ <ul>
+ <li>Quick derivation of the quadratic equation by completing the square</li>
+ <li>Published On: 2024-03-26 15:36</li>
+ <li>Tags:
+
+ <a href='/tags/mathematics.html'>mathematics</a>
+
+ </ul>
+
+
<li><a href="/posts/2023-04-30-n-body-simulation.html">n-body solution generator</a></li>
<ul>
<li>n-body solution generator and solver</li>