Free Math & Algebra Help

One of the most asked questions in algebra class is "How do you complete the square in a math problem?" Completing the square seems to be one of the most difficult tasks in an algebra class, but it is actually fairly easy if you remember a series of steps. The steps are shown below:

Solve 2x² + 3x - 8 = 0 by completing the square.

Step 1 - Isolate the x-squared and x-terms on one side of = .

Step 2 - Divide all terms on both sides by the coefficient on x² . In this case divide by 2. Simplify the result. 


Step 3 - Take 1/2 of the coefficient of the x-term. Square this amount and then add this result to both sides of the equation. Simply the sum on the right side of =.

1/2 of 3/2 = 1/2 * 3/2 = 3/4
(3/4)² = (3/4)*(3/4) = 9/16

x² + (3/2)x + 9/16 = 4 + 9/16

x² + (3/2)x + 9/16 = 64/16 + 9/16

x² + (3/2)x + 9/16 = 73/16

Step 4 - Factor the left side of the equation. Write in perfect square form.

(x + 3/4)(x + 3/4) = 73/16 which may be written as
(x + 3/4)² = 73/16

Step 5 - Solve this equation by extracting square roots. This amounts to taking the square root of both sides and applying a +/- sign to the radical.