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\sqrt{x+6}-1-\left(-1\right)=-\left(-1\right)
Add 1 to both sides of the equation.
\sqrt{x+6}=-\left(-1\right)
Subtracting -1 from itself leaves 0.
\sqrt{x+6}=1
Subtract -1 from 0.
x+6=1
Square both sides of the equation.
x+6-6=1-6
Subtract 6 from both sides of the equation.
x=1-6
Subtracting 6 from itself leaves 0.
x=-5
Subtract 6 from 1.