Quadratic Equations
12-1Quadratic Equations with Perfect Squares
Overview
Solve x² = k by taking the square root of both sides: x = ±√k.
Key ideas
- There are usually two solutions: positive and negative roots.
- No real solution when k < 0.
- Works for any (x + h)² = k form too.
Worked examples
Example 1
Problem. Solve x² = 49.
Solution. x = ±7.
Example 2
Problem. Solve (x − 2)² = 9.
Solution. x − 2 = ±3 → x = 5 or −1.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve x² = 64.
- 2.
Solve (x + 1)² = 16.
- 3.
Solve x² = 0.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: (x − 3)² = 25.
- 2.
Solve: 4(x + 2)² = 36.