Solve -1/2(x+8)^2+18=10

$$- \frac { 1 } { 2 } ( x + 8 ) ^ { 2 } + 18 = 10$$

Solve for x

$$x=-4$$

$$x=-12$$

Steps by Finding Square Root

Subtract 18 from both sides of the equation.

$$-\frac{1}{2}\left(x+8\right)^{2}+18-18=10-18$$

Subtracting 18 from itself leaves 0.

$$-\frac{1}{2}\left(x+8\right)^{2}=10-18$$

Subtract 18 from 10.

$$-\frac{1}{2}\left(x+8\right)^{2}=-8$$

Multiply both sides by -2.

$$\frac{-\frac{1}{2}\left(x+8\right)^{2}}{-\frac{1}{2}}=-\frac{8}{-\frac{1}{2}}$$

Dividing by -\frac{1}{2} undoes the multiplication by -\frac{1}{2}.

$$\left(x+8\right)^{2}=-\frac{8}{-\frac{1}{2}}$$

Divide -8 by -\frac{1}{2} by multiplying -8 by the reciprocal of -\frac{1}{2}.

$$\left(x+8\right)^{2}=16$$

Take the square root of both sides of the equation.

$$x+8=4 x+8=-4$$

Subtract 8 from both sides of the equation.

$$x+8-8=4-8 x+8-8=-4-8$$

Subtracting 8 from itself leaves 0.

$$x=4-8 x=-4-8$$

Subtract 8 from 4.

$$x=-4$$

Subtract 8 from -4.

$$x=-12$$

The equation is now solved.

$$x=-4 x=-12$$