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feat(guide): Import guide in to the client app
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---
title: Completing the Square
---
## Completing the Square
[Guide]: add article for completing the square (#19166) * [Guide]: add article for completing the square Add article with step by step guide on solving quadratic equations using the completing the square method * removed stub information
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<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
feat(guide): Import guide in to the client app
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[Guide]: add article for completing the square (#19166) * [Guide]: add article for completing the square Add article with step by step guide on solving quadratic equations using the completing the square method * removed stub information
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The completing the square method is one of the many methods for solving a <a href='https://guide.freecodecamp.org/mathematics/quadratic-equations' target='_blank'>quadratic eduation</a>. It involves changing the form of the equation so that the left side becomes a perfect square.
feat(guide): Import guide in to the client app
2018-10-04 13:47:55 +00:00
[Guide]: add article for completing the square (#19166) * [Guide]: add article for completing the square Add article with step by step guide on solving quadratic equations using the completing the square method * removed stub information
2018-10-15 01:57:50 +00:00
A quadratic equation generally takes the form: <em>ax<sup>2</sup> + bx + c</em> = 0. In solving the above, follow the following steps:
1. Move the constant value to the Right Hand Side of the equation so it becomes: <br>
<pre><em>ax<sup>2</sup> + bx = -c</em></pre>
2. Make the coefficient of x<sup>2</sup> equal to 1 by dividing both sides of the equation by <em>a</em> so that we now have: <br>
<pre>x<sup>2</sup> + (<sup>b</sup>/<sub>a</sub>)x = - (<sup>c</sup>/<sub>a</sub>)</pre>
3. Next, add the square of half of the coefficient of the <em>x</em>-term to both sides of the equation: <br>
<pre>x<sup>2</sup> + (<sup>b</sup>/<sub>a</sub>)x + (<sup>b</sup>/<sub>2a</sub>)<sup>2</sup> = (<sup>b</sup>/<sub>2a</sub>)<sup>2</sup> - (<sup>c</sup>/<sub>a</sub>)</pre>
4. Completing the square on the Left Hand Side and simplifying the Right Hand Side of the above equation, we have:
<pre>(x<sup></sup> + <sup>b</sup>/<sub>2a</sub>)<sup>2</sup> = (<sup>b<sup>2</sup></sup>/<sub>4a<sup>2</sup></sub>) - (<sup>c</sup>/<sub>a</sub>)</pre>
5. Further simplpfying the Right Hand Side,
<pre>(x<sup></sup> + <sup>b</sup>/<sub>2a</sub>)<sup>2</sup> = (b<sup>2</sup> - 4ac)/4a<sup>2</sup> </pre>
6. Finding the square root of both sides of the equation,
<pre>x<sup></sup> + <sup>b</sup>/<sub>2a</sub> = &radic;(b<sup>2</sup> - 4ac) &divide; 2a </pre>
7. By making x the subject of our formula, we are able to solve for its value completely:
<pre>x<sup></sup> = -b &#177; &radic;(b<sup>2</sup> - 4ac) &divide; 2a </pre>
feat(guide): Import guide in to the client app
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#### More Information:
<!-- Please add any articles you think might be helpful to read before writing the article -->
[Guide]: add article for completing the square (#19166) * [Guide]: add article for completing the square Add article with step by step guide on solving quadratic equations using the completing the square method * removed stub information
2018-10-15 01:57:50 +00:00
* [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/completing-the-square)
* [Maths is Fun](https://www.mathsisfun.com/algebra/completing-square.html)
feat(guide): Import guide in to the client app
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