Practice Completing the Square in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A technique for rewriting ax^2 + bx + c in vertex form a(x - h)^2 + k by adding and subtracting the value \left(\frac{b}{2a}\right)^2 to create a perfect square trinomial.

Imagine you have x^2 + 6x and want a perfect square. A perfect square like (x + 3)^2 = x^2 + 6x + 9 needs that extra +9. So you add 9 and subtract 9 to keep the expression equal—then group the perfect square part.

Example 1

medium
Rewrite x^2 + 6x + 2 in vertex form by completing the square.

Example 2

hard
Solve x^2 - 4x - 5 = 0 by completing the square.

Example 3

easy
What number completes the square for x^2 + 10x + \,\_\,?

Example 4

medium
Rewrite x^2 - 8x + 20 in vertex form.
← Back to Completing the Square Worked Examples Formula Explained