Solve the equation. Check all proposed solutions. Show work in solving and in checking.
√(x+7)-5=x
√(x+7) = x + 5 (Add 5 to both sides)
(√(x+7))^{2} = (x + 5)^{2 } (Square both sides of the equation)
x+7 = x^{2} + 10x + 25 (Multiply out the squares)
0 = x^{2} + 9x +18 (Combine like terms into a quadratic equation)
0 = (x+6)(x+3) (Factor the quadratic)
x= -6, -3
Check by plugging -3 and -6 into the original equation One of the solutions works, one doesn't.