Solving x² = p by square roots, step by step
When a quadratic is already a bare square, there is nothing to factor.
The question
Solve 7x² = 28 by taking square roots.
Solve 7x² = 28
x² = 28 ÷ 7=4
x = ±√4=±2
x = 2orx = −2
- First divide by 7 to get the square alone: x² = 28 ÷ 7 = 4.
- Now take the square root of both sides. Two different numbers square to the same thing — 2 × 2 and (−2) × (−2) both give 4 — so the square root question has TWO answers, and writing only the positive one loses half of it. So x = ±√4 = ±2.
- So x = 2 or x = −2 — both roots.
How it works.
- 01
First divide by 7 to get the square alone: x² = 28 ÷ 7 = 4.
- 02
Now take the square root of both sides. Two different numbers square to the same thing — 2 × 2 and (−2) × (−2) both give 4 — so the square root question has TWO answers, and writing only the positive one loses half of it. So x = ±√4 = ±2.
- 03
So x = 2 or x = −2 — both roots.