We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.

High School: Algebra

High School: Algebra

Reasoning with Equations and Inequalities A-REI.4a

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (xp)2 = q that has the same solutions. Derive the quadratic formula from this form.

This is a sneaky and fun way to solve unruly quadratic equations. It involves creating and factoring a "perfect square" (meaning, a quadratic expression whose two linear factors are the same). Let's solve the same equation as we did before: x2 + x – 12 = 0.

First, add 12 to both sides: x2 + x = 12. Next, complete the square by making the left side a perfect square. To do that, we take b, divide by 2, and square the result. In this case, our b = 1, which ends up being ¼. Add this to both sides of the equation.

The left side is a perfect square because its two linear factors are the same: x + ½. Therefore, we can re-write the left side of the equation and simplify the right-hand side.

From there, we can square root both sides and subtract both sides by ½.

x = 3, -4

Aligned Resources

    More standards from High School: Algebra - Reasoning with Equations and Inequalities