Solve (a-9/5)^2+64/25=16

$$( a - \frac { 9 } { 5 } ) ^ { 2 } + \frac { 64 } { 25 } = 16$$

Solve for a

$$a = \frac{4 \sqrt{21} + 9}{5} \approx 5.466060556$$

$$a=\frac{9-4\sqrt{21}}{5}\approx -1.866060556$$

Steps by Finding Square Root

Subtract \frac{64}{25} from both sides of the equation.

$$\left(a-\frac{9}{5}\right)^{2}+\frac{64}{25}-\frac{64}{25}=16-\frac{64}{25}$$

Subtracting \frac{64}{25} from itself leaves 0.

$$\left(a-\frac{9}{5}\right)^{2}=16-\frac{64}{25}$$

Subtract \frac{64}{25} from 16.

$$\left(a-\frac{9}{5}\right)^{2}=\frac{336}{25}$$

Take the square root of both sides of the equation.

$$a-\frac{9}{5}=\frac{4\sqrt{21}}{5} a-\frac{9}{5}=-\frac{4\sqrt{21}}{5}$$

Add \frac{9}{5} to both sides of the equation.

$$a-\frac{9}{5}-\left(-\frac{9}{5}\right)=\frac{4\sqrt{21}}{5}-\left(-\frac{9}{5}\right) a-\frac{9}{5}-\left(-\frac{9}{5}\right)=-\frac{4\sqrt{21}}{5}-\left(-\frac{9}{5}\right)$$

Subtracting -\frac{9}{5} from itself leaves 0.

$$a=\frac{4\sqrt{21}}{5}-\left(-\frac{9}{5}\right) a=-\frac{4\sqrt{21}}{5}-\left(-\frac{9}{5}\right)$$

Subtract -\frac{9}{5} from \frac{4\sqrt{21}}{5}.

$$a=\frac{4\sqrt{21}+9}{5}$$

Subtract -\frac{9}{5} from -\frac{4\sqrt{21}}{5}.

$$a=\frac{9-4\sqrt{21}}{5}$$

The equation is now solved.

$$a=\frac{4\sqrt{21}+9}{5} a=\frac{9-4\sqrt{21}}{5}$$