Question

Solve the following quadratic equation for all values of xx in simplest form.
2, left parenthesis, x, minus, 7, right parenthesis, squared, minus, 31, equals, 1
2(x−7)
2
−31=
1

Answer 1

Solve 2(x − 7)^2 − 31 = 1.

Step 1: Add 31 to both sides:
2(x − 7)^2 = 32

Step 2: Divide by 2:
(x − 7)^2 = 16

Step 3: Take square roots:
x − 7 = ±4

So x = 7 ± 4, giving x = 11 or x = 3.