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\sqrt{x+8}-5-\left(-5\right)=-2-\left(-5\right)
Add 5 to both sides of the equation.
\sqrt{x+8}=-2-\left(-5\right)
Subtracting -5 from itself leaves 0.
\sqrt{x+8}=3
Subtract -5 from -2.
x+8=9
Square both sides of the equation.
x+8-8=9-8
Subtract 8 from both sides of the equation.
x=9-8
Subtracting 8 from itself leaves 0.
x=1
Subtract 8 from 9.