Completing the Square Worksheets

Free Completing the Square Worksheet Library (with Answer Keys)

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Each place value worksheet can be downloaded as a PDF file that is easy to print or share online. All worksheets also include a complete answer key on the last page.

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Completing the Square Worksheets

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Completing the Square Review

Solving problems by completing the square is when you use a specific strategy for solving equations of the form ax² + bx + c = 0.

You can solve any quadratic equation in this form by following the following 3-steps for completing the square:

• Step #1: Rearrange the equation to place all of the constants on one side.

• Step #2: + (b/2)² to both sides.

• Step #3: Factor and solve.

For example, let’s say that we wanted to find the solutions of the equation x² - 6x -16 = 0 by completing the square. In this case, we could find the solutions by using the 3-step method as follows:

Step #1: Rearrange the equation to place all of the constants on one side.

For our first step, we can start by identifying that the equation x² - 6x -16 = 0 is in ax² +bx + c = 0 form, with a=1, b=-6, and c=-16.

We can complete the first step by moving all of the constants to one side of the equation as follows:

• x² - 6x -16 (+16) = 0 (+16)

• x² - 6x = 16

Our result is the equation:

• x² - 6x = 16

Step #2: + (b/2)² to both sides.

In this example, b=-6, so we can add (b/2)² to both sides of the equation by substituting b with -6 as follows:

• (-6/2)² = (-3)² = 9

• x² - 6x = 16

• x² - 6x + 9 = 16 + 9

• x² - 6x + 9 = 25

Step #3: Factor and solve.

For our final step, we simply have to factor and solve the trinomial on the left side of the equation as follows:

• x² - 6x + 9 = (x-3)(x-3)

• x² - 6x + 9 = (x-3)²

• x² - 6x + 9 = 25

• (x-3)² = 25

• √[(x-3)²] = √[25]

• x -3 = ± 5

Now we just have to solve for x in each of the following equations:

• x - 3 = 5 → x = 8

• x - 3 = -5 → x = -2

Final Answer: x = 8, x = -2

Do you need more help with completing the square using our 3-step method? Click here to check out our free step-by-step student guide to completing the square to work through a few more practice problems.