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\sqrt{q+89}-55-\left(-55\right)=-41-\left(-55\right)
Add 55 to both sides of the equation.
\sqrt{q+89}=-41-\left(-55\right)
Subtracting -55 from itself leaves 0.
\sqrt{q+89}=14
Subtract -55 from -41.
q+89=196
Square both sides of the equation.
q+89-89=196-89
Subtract 89 from both sides of the equation.
q=196-89
Subtracting 89 from itself leaves 0.
q=107
Subtract 89 from 196.