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Solve ,equation ,check all proposed solutions Show work

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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 = x2 + 10x + 25            (Multiply out the squares)
 
0 = x2 + 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.

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