Solve ,equation ,check all proposed solutions Show work

Question

Solve the equation. Check all proposed solutions. Show work in solving and in checking.

 

√(x+7)-5=x

Answer 1

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.