Question

Square root of (x+6)-4=x, extraneous or not

Answer 1

x = -2 or x=-5

Explanation:

sqrt(x+6)-4 = x

sqrt(x+6) = x+4

square both sides

x+6 = x²+8x+16

x²+7x+10 = 0

(x+2)(x+5) = 0

x = -2 or x=-5

Substitute in original equation

x=-2 +/- sqrt(-2+6)-4 = 2-4 = -2 checks

x=-5 +/- sqrt(-5+6)-4 = -1-4 = -5 checks