gaspersic/freeCodeCamp
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

[Guide]: add article for completing the square (#19166)

Browse Source 
* [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
This commit is contained in:
Oluwafunmito Blessed
2018-10-15 02:57:50 +01:00
committed by Randell Dawson
parent fcec866b99
commit 43174378c9
1 changed files with 27 additions and 5 deletions
Download Patch File Download Diff File Expand all files Collapse all files

32
client/src/pages/guide/english/mathematics/completing-the-square/index.md
View File

@ -3,13 +3,35 @@ title: Completing the Square
---
## Completing the Square
This is a stub. <a href='https://github.com/freecodecamp/guides/tree/master/src/pages/mathematics/completing-the-square/index.md' target='_blank' rel='nofollow'>Help our community expand it</a>.
<a href='https://github.com/freecodecamp/guides/blob/master/README.md' target='_blank' rel='nofollow'>This quick style guide will help ensure your pull request gets accepted</a>.
<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
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.
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>
#### More Information:
<!-- Please add any articles you think might be helpful to read before writing the article -->
* [Varsity Tutors](https://www.varsitytutors.com/hotmath/hotmath_help/topics/completing-the-square)
* [Maths is Fun](https://www.mathsisfun.com/algebra/completing-square.html)