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\sqrt{x+10}-7-\left(-7\right)=-5-\left(-7\right)
Add 7 to both sides of the equation.
\sqrt{x+10}=-5-\left(-7\right)
Subtracting -7 from itself leaves 0.
\sqrt{x+10}=2
Subtract -7 from -5.
x+10=4
Square both sides of the equation.
x+10-10=4-10
Subtract 10 from both sides of the equation.
x=4-10
Subtracting 10 from itself leaves 0.
x=-6
Subtract 10 from 4.