Solve (lambda+1/2)^2-1/8=0

$$( \lambda + \frac { 1 } { 2 } ) ^ { 2 } - \frac { 1 } { 8 } = 0$$

Solve for λ

$$\lambda =\frac{\sqrt{2}}{4}-\frac{1}{2}\approx -0.146446609$$

$$\lambda =-\frac{\sqrt{2}}{4}-\frac{1}{2}\approx -0.853553391$$

Steps by Finding Square Root

Add \frac{1}{8} to both sides of the equation.

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

Subtracting \frac{1}{8} from itself leaves 0.

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

Take the square root of both sides of the equation.

$$\lambda +\frac{1}{2}=\frac{\sqrt{2}}{4} \lambda +\frac{1}{2}=-\frac{\sqrt{2}}{4}$$

Subtract \frac{1}{2} from both sides of the equation.

$$\lambda +\frac{1}{2}-\frac{1}{2}=\frac{\sqrt{2}}{4}-\frac{1}{2} \lambda +\frac{1}{2}-\frac{1}{2}=-\frac{\sqrt{2}}{4}-\frac{1}{2}$$

Subtracting \frac{1}{2} from itself leaves 0.

$$\lambda =\frac{\sqrt{2}}{4}-\frac{1}{2} \lambda =-\frac{\sqrt{2}}{4}-\frac{1}{2}$$