Solving quadratics by square roots, step by step
Some quadratics do not need factoring.
The question
Solve (x − 1)² = 25 by taking square roots.
Solve (x − 1)² = 25
x − 1 = ±5
x = 1 ± 5
x = 6orx = −4
- Take the square root of both sides. Two different numbers square to the same thing — 5 × 5 and (−5) × (−5) both give 25 — so the square root question has TWO answers, and writing only the positive one loses half of it. So x − 1 = ±√25 = ±5.
- Then add 1 to both sides: x = 1 ± 5.
- So x = 6 or x = −4 — both roots.
How it works.
- 01
Take the square root of both sides. Two different numbers square to the same thing — 5 × 5 and (−5) × (−5) both give 25 — so the square root question has TWO answers, and writing only the positive one loses half of it. So x − 1 = ±√25 = ±5.
- 02
Then add 1 to both sides: x = 1 ± 5.
- 03
So x = 6 or x = −4 — both roots.