Explain the steps used to solve x - 2 = v(x + 10) and check for extraneous solutions.

Question

x - 2 = √(x + 10) 


Square both sides

(x - 2)² = (√(x + 10))²
(x - 2)² = (x + 10)   ← square and square root would will net off each other


Remove brackets

x² - 4x + 2² = x + 10
x² - 4x + 4 = x + 10


minus x + 10 on both sides

x² - 4x + 4 - x - 10 = 0
x² - 5x - 6 = 0


Factorise the left side

(x - 6)(x + 1) = 0


Apply zero product property 

x -6 = 0  or  x +1 = 0


Solve x

x = 6 or x = -1


x = 6 or x = -1

She should use 12/3 to measure