Solve (4/5+a)^2+9/25=4

$$( \frac { 4 } { 5 } + a ) ^ { 2 } + \frac { 9 } { 25 } = 4$$

Solve for a

$$a = \frac{\sqrt{91} - 4}{5} \approx 1.107878403$$

$$a=\frac{-\sqrt{91}-4}{5}\approx -2.707878403$$

Steps by Finding Square Root

Subtract \frac{9}{25} from both sides of the equation.

$$\left(a+\frac{4}{5}\right)^{2}+\frac{9}{25}-\frac{9}{25}=4-\frac{9}{25}$$

Subtracting \frac{9}{25} from itself leaves 0.

$$\left(a+\frac{4}{5}\right)^{2}=4-\frac{9}{25}$$

Subtract \frac{9}{25} from 4.

$$\left(a+\frac{4}{5}\right)^{2}=\frac{91}{25}$$

Take the square root of both sides of the equation.

$$a+\frac{4}{5}=\frac{\sqrt{91}}{5} a+\frac{4}{5}=-\frac{\sqrt{91}}{5}$$

Subtract \frac{4}{5} from both sides of the equation.

$$a+\frac{4}{5}-\frac{4}{5}=\frac{\sqrt{91}}{5}-\frac{4}{5} a+\frac{4}{5}-\frac{4}{5}=-\frac{\sqrt{91}}{5}-\frac{4}{5}$$

Subtracting \frac{4}{5} from itself leaves 0.

$$a=\frac{\sqrt{91}}{5}-\frac{4}{5} a=-\frac{\sqrt{91}}{5}-\frac{4}{5}$$

Subtract \frac{4}{5} from \frac{\sqrt{91}}{5}.

$$a=\frac{\sqrt{91}-4}{5}$$

Subtract \frac{4}{5} from -\frac{\sqrt{91}}{5}.

$$a=\frac{-\sqrt{91}-4}{5}$$

The equation is now solved.

$$a=\frac{\sqrt{91}-4}{5} a=\frac{-\sqrt{91}-4}{5}$$