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Completing the Square

Completing the Square

Author: Rachel Kaplan
Description:

Learn how to solve a quadratic equation by a new method called completing the square.

Sometimes a quadratic equation is not easily factorable. By completing the square, you can successfully solve any quadratic equation to you heart's desire. I, too had long struggled with the horrors of completing the square, however, through this learning packet, you will become a pro in no time....

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Tutorial

First watch the videos below on how and why to complete the square. And no, we don't just do it for fun...even though it is extremely enjoyable.

....Then review what we learned in the videos with the step-by-step procedure found at the bottom of the page.

 

A Quick Note...

 Please note that at one point in the video above, when we are supposed to solve for "a," "x" is written instead. A minor error. 

Step by Step

Step 1: Subtract any constants from both sides (remember to leave a space)

Step 2: Solve for "a"

Step 3: Square "a" and add it to the left side of the equation to complete into a perfect square

Step 4:  Add the same number to the right side of the equation

Step 5: Re-write the left side into (x-a)2 form

Step 6: Take the square root of both sides

Step 7: Add "a" to both sides (remember the plus/minus sign!)

Examples

For a great site with example problems and hints, check out the link below:

http://www.algebralab.org/lessons/lesson.aspx?file=algebra_completingthesquare.xml