Solve 1/2(x+6)^2-5=123

$$\frac { 1 } { 2 } ( x + 6 ) ^ { 2 } - 5 = 123$$

Solve for x

$$x=10$$

$$x=-22$$

Steps by Finding Square Root

Add 5 to both sides of the equation.

$$\frac{1}{2}\left(x+6\right)^{2}-5+5=123+5$$

Subtracting 5 from itself leaves 0.

$$\frac{1}{2}\left(x+6\right)^{2}=123+5$$

Add 123 to 5.

$$\frac{1}{2}\left(x+6\right)^{2}=128$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}\left(x+6\right)^{2}}{\frac{1}{2}}=\frac{128}{\frac{1}{2}}$$

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

$$\left(x+6\right)^{2}=\frac{128}{\frac{1}{2}}$$

Divide 128 by \frac{1}{2} by multiplying 128 by the reciprocal of \frac{1}{2}.

$$\left(x+6\right)^{2}=256$$

Take the square root of both sides of the equation.

$$x+6=16 x+6=-16$$

Subtract 6 from both sides of the equation.

$$x+6-6=16-6 x+6-6=-16-6$$

Subtracting 6 from itself leaves 0.

$$x=16-6 x=-16-6$$

Subtract 6 from 16.

$$x=10$$

Subtract 6 from -16.

$$x=-22$$

The equation is now solved.

$$x=10 x=-22$$