Solve (1/2L)^2+1/2=2

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

Solve for L

$$L=\sqrt{6}\approx 2.449489743$$

$$L=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Expand \left(\frac{1}{2}L\right)^{2}.

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

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4}L^{2}+\frac{1}{2}=2$$

Subtract \frac{1}{2} from both sides.

$$\frac{1}{4}L^{2}=2-\frac{1}{2}$$

Subtract \frac{1}{2} from 2 to get \frac{3}{2}.

$$\frac{1}{4}L^{2}=\frac{3}{2}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$L^{2}=\frac{3}{2}\times 4$$

Multiply \frac{3}{2} and 4 to get 6.

$$L^{2}=6$$

Take the square root of both sides of the equation.

$$L=\sqrt{6} L=-\sqrt{6}$$