Solve (a-1/3)^2=-47/9

$$( a - \frac { 1 } { 3 } ) ^ { 2 } = - \frac { 47 } { 9 }$$

Solve for a

$$a=\frac{-\sqrt{47}i+1}{3}\approx 0.333333333-2.2852182i$$

$$a=\frac{1+\sqrt{47}i}{3}\approx 0.333333333+2.2852182i$$

Steps by Finding Square Root

Add \frac{1}{3} to both sides of the equation.

$$a-\frac{1}{3}-\left(-\frac{1}{3}\right)=\frac{\sqrt{47}i}{3}-\left(-\frac{1}{3}\right) a-\frac{1}{3}-\left(-\frac{1}{3}\right)=-\frac{\sqrt{47}i}{3}-\left(-\frac{1}{3}\right)$$

Subtracting -\frac{1}{3} from itself leaves 0.

$$a=\frac{\sqrt{47}i}{3}-\left(-\frac{1}{3}\right) a=-\frac{\sqrt{47}i}{3}-\left(-\frac{1}{3}\right)$$

Subtract -\frac{1}{3} from \frac{i\sqrt{47}}{3}.

$$a=\frac{1+\sqrt{47}i}{3}$$

Subtract -\frac{1}{3} from -\frac{i\sqrt{47}}{3}.

$$a=\frac{-\sqrt{47}i+1}{3}$$

The equation is now solved.

$$a=\frac{1+\sqrt{47}i}{3} a=\frac{-\sqrt{47}i+1}{3}$$