Solve 2(-a-1)^2=5

$$2 ( - a - 1 ) ^ { 2 } = 5$$

Solve for a

$$a=\frac{\sqrt{10}}{2}-1\approx 0.58113883$$

$$a=-\frac{\sqrt{10}}{2}-1\approx -2.58113883$$

Steps by Finding Square Root

Divide both sides by 2.

$$\frac{2\left(-a-1\right)^{2}}{2}=\frac{5}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\left(-a-1\right)^{2}=\frac{5}{2}$$

Take the square root of both sides of the equation.

$$-a-1=\frac{\sqrt{10}}{2} -a-1=-\frac{\sqrt{10}}{2}$$

Add 1 to both sides of the equation.

$$-a-1-\left(-1\right)=\frac{\sqrt{10}}{2}-\left(-1\right) -a-1-\left(-1\right)=-\frac{\sqrt{10}}{2}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$-a=\frac{\sqrt{10}}{2}-\left(-1\right) -a=-\frac{\sqrt{10}}{2}-\left(-1\right)$$

Subtract -1 from \frac{\sqrt{10}}{2}.

$$-a=\frac{\sqrt{10}}{2}+1$$

Subtract -1 from -\frac{\sqrt{10}}{2}.

$$-a=-\frac{\sqrt{10}}{2}+1$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{\frac{\sqrt{10}}{2}+1}{-1} \frac{-a}{-1}=\frac{-\frac{\sqrt{10}}{2}+1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{\frac{\sqrt{10}}{2}+1}{-1} a=\frac{-\frac{\sqrt{10}}{2}+1}{-1}$$

Divide \frac{\sqrt{10}}{2}+1 by -1.

$$a=-\frac{\sqrt{10}}{2}-1$$

Divide -\frac{\sqrt{10}}{2}+1 by -1.

$$a=\frac{\sqrt{10}}{2}-1$$

The equation is now solved.

$$a=-\frac{\sqrt{10}}{2}-1 a=\frac{\sqrt{10}}{2}-1$$