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\sqrt{x+8}-9-\left(-9\right)=-4-\left(-9\right)
Add 9 to both sides of the equation.
\sqrt{x+8}=-4-\left(-9\right)
Subtracting -9 from itself leaves 0.
\sqrt{x+8}=5
Subtract -9 from -4.
x+8=25
Square both sides of the equation.
x+8-8=25-8
Subtract 8 from both sides of the equation.
x=25-8
Subtracting 8 from itself leaves 0.
x=17
Subtract 8 from 25.