Solve 9/4+(2-a)^2=5

$$\frac { 9 } { 4 } + ( 2 - a ) ^ { 2 } = 5$$

Solve for a

$$a=-\frac{\sqrt{11}}{2}+2\approx 0.341687605$$

$$a=\frac{\sqrt{11}}{2}+2\approx 3.658312395$$

Steps by Finding Square Root

Subtract \frac{9}{4} from both sides of the equation.

$$\left(-a+2\right)^{2}+\frac{9}{4}-\frac{9}{4}=5-\frac{9}{4}$$

Subtracting \frac{9}{4} from itself leaves 0.

$$\left(-a+2\right)^{2}=5-\frac{9}{4}$$

Subtract \frac{9}{4} from 5.

$$\left(-a+2\right)^{2}=\frac{11}{4}$$

Take the square root of both sides of the equation.

$$-a+2=\frac{\sqrt{11}}{2} -a+2=-\frac{\sqrt{11}}{2}$$

Subtract 2 from both sides of the equation.

$$-a+2-2=\frac{\sqrt{11}}{2}-2 -a+2-2=-\frac{\sqrt{11}}{2}-2$$

Subtracting 2 from itself leaves 0.

$$-a=\frac{\sqrt{11}}{2}-2 -a=-\frac{\sqrt{11}}{2}-2$$

Subtract 2 from \frac{\sqrt{11}}{2}.

$$-a=\frac{\sqrt{11}}{2}-2$$

Subtract 2 from -\frac{\sqrt{11}}{2}.

$$-a=-\frac{\sqrt{11}}{2}-2$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{\frac{\sqrt{11}}{2}-2}{-1} \frac{-a}{-1}=\frac{-\frac{\sqrt{11}}{2}-2}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{\frac{\sqrt{11}}{2}-2}{-1} a=\frac{-\frac{\sqrt{11}}{2}-2}{-1}$$

Divide \frac{\sqrt{11}}{2}-2 by -1.

$$a=-\frac{\sqrt{11}}{2}+2$$

Divide -\frac{\sqrt{11}}{2}-2 by -1.

$$a=\frac{\sqrt{11}}{2}+2$$

The equation is now solved.

$$a=-\frac{\sqrt{11}}{2}+2 a=\frac{\sqrt{11}}{2}+2$$