Solving (x − h)² = k by square roots, step by step
A shifted square adds one move to the square root method.
The question
Solve (x + 5)² = 9 by taking square roots.
Solve (x + 5)² = 9
x + 5 = ±3
x = −5 ± 3
x = −2orx = −8
- Take the square root of both sides. Two different numbers square to the same thing — 3 × 3 and (−3) × (−3) both give 9 — so the square root question has TWO answers, and writing only the positive one loses half of it. So x + 5 = ±√9 = ±3.
- Then subtract 5 from both sides: x = −5 ± 3.
- So x = −2 or x = −8 — both roots.
How it works.
- 01
Take the square root of both sides. Two different numbers square to the same thing — 3 × 3 and (−3) × (−3) both give 9 — so the square root question has TWO answers, and writing only the positive one loses half of it. So x + 5 = ±√9 = ±3.
- 02
Then subtract 5 from both sides: x = −5 ± 3.
- 03
So x = −2 or x = −8 — both roots.