This helps you solve for x in quadratic equations of the form .

Subtract c from both sides of the equation.
If a is not 1, divide both sides by a. (Do each term appropriately.)
Cut b in half (mentally).
Square the result (mentally).
Add that result to both sides of the equation (actually).
Factor the perfect square trinomial on the left hand side of the equation. Make a ( ...............)².
Square root both sides (Recall that when you square root the right side you include ±.)
Split the problem.
Get x by itself. (Round off to the nearest 100^th.)

You will get two answers most of the time.

Completing the square is only one method for solving quadratic equations. You can also use the Quadratic Formula.

Examples Done by Mr. Vizza

Directions: In the following equation, please solve for x by completing the square.

Step 1

Step 2

a=1, therefore, there is no division necessary

Step 3

6/2=3

Step 4

3^{^²}=9

Step 5

Step 6

Step 7

Step 8 (Note: We also simplify the radical on the right hand side using a factoring technique.)

Step 9

Problems that You Should Practice

Directions: In the following equation, please solve for x by completing the square. If there is no solution to the equation, please indicate so by stating "null set".

Directions: Please answer the following questions.

13. A rectangle has an area of twenty-four, which is the sum of a number squared and four times that number. What are the dimensions of the rectangle? (Solve this by completing the square.)

Writing Exercise

Directions: Please write 1-2 paragraphs that thoroughly address the following.

1. How are the processes of completing the square and performing the quadratic formula related? Are they the same process? If they are not the same process, why do they yield the same answer?

Additional Supportive Links

Click below for more great advice and examples on:

University of Hawaii's page

University of Texas at El Paso's page

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