Solve for x:
sqrt(x + 4) = x - 2
Raise both sides to the power of two:
x + 4 = (x - 2)^2
Expand out terms of the right hand side:
x + 4 = x^2 - 4 x + 4
Subtract x^2 - 4 x + 4 from both sides:
5 x - x^2 = 0
Factor x and constant terms from the left hand side:
-x (x - 5) = 0
Multiply both sides by -1:
x (x - 5) = 0
Split into two equations:
x - 5 = 0 or x = 0
Add 5 to both sides:
x = 5 or x = 0
So, x = 0 discard. Or x = 5