Question

Addison solves the equation below by first squaring both sides of the equation.

Answer 1

2x - 1 = √(8 - x)

Squaring

(2x - 1)² = 8 - x

4x² - 4x + 1 = 8 - x

4x² - 3x -7 = 0

(4x - 7)(x + 1) = 0

4x = 7 or x = -1

x = 7/4 or x=-1

x=7/4 checks, 2(7/4)-1 = 10/4 = 5/2,  √(8-7/4)=√(25/4) = 5/2, good

x=-1 fails, 2(-1) - 1 = -3, can't be a principal square root

Answer: -1  is extraneous