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

√(x+7)-5=x

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

√(x+7)-5=x

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Olney, MD

√(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.

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