Solve 1/2(x+2)^2=7

$$\frac { 1 } { 2 } ( x + 2 ) ^ { 2 } = 7$$

Solve for x

$$x=\sqrt{14}-2\approx 1.741657387$$

$$x=-\left(\sqrt{14}+2\right)\approx -5.741657387$$

Steps by Finding Square Root

Multiply both sides by 2.

$$\frac{\frac{1}{2}\left(x+2\right)^{2}}{\frac{1}{2}}=\frac{7}{\frac{1}{2}}$$

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

$$\left(x+2\right)^{2}=\frac{7}{\frac{1}{2}}$$

Divide 7 by \frac{1}{2} by multiplying 7 by the reciprocal of \frac{1}{2}.

$$\left(x+2\right)^{2}=14$$

Take the square root of both sides of the equation.

$$x+2=\sqrt{14} x+2=-\sqrt{14}$$

Subtract 2 from both sides of the equation.

$$x+2-2=\sqrt{14}-2 x+2-2=-\sqrt{14}-2$$

Subtracting 2 from itself leaves 0.

$$x=\sqrt{14}-2 x=-\sqrt{14}-2$$