Quadratic Equations
12-2Completing the Square
Overview
Turn x² + bx into a perfect square by adding (b/2)². Then solve by taking the square root.
Key ideas
- Move constant to the right side first.
- Add (b/2)² to both sides.
- Factor the perfect-square trinomial; take roots.
Worked examples
Example 1
Problem. Solve x² + 6x = 7.
Solution. Add (6/2)² = 9: x² + 6x + 9 = 16 → (x + 3)² = 16 → x = 1 or −7.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve x² + 4x = 5.
- 2.
Solve x² − 8x = 9.
- 3.
Solve x² + 2x − 8 = 0.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve by completing the square: x² + 6x − 7 = 0.
- 2.
Solve by completing the square: x² − 4x + 1 = 0.