Solve A^2=A^2/4-81

$$A ^ { 2 } = \frac { A ^ { 2 } } { 4 } - 81$$

Solve for A

$$A=-6\sqrt{3}i\approx -0-10.392304845i$$

$$A=6\sqrt{3}i\approx 10.392304845i$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$4A^{2}=A^{2}-324$$

Subtract A^{2} from both sides.

$$4A^{2}-A^{2}=-324$$

Combine 4A^{2} and -A^{2} to get 3A^{2}.

$$3A^{2}=-324$$

Divide both sides by 3.

$$A^{2}=\frac{-324}{3}$$

Divide -324 by 3 to get -108.

$$A^{2}=-108$$

The equation is now solved.

$$A=6\sqrt{3}i A=-6\sqrt{3}i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$4A^{2}=A^{2}-324$$

Subtract A^{2} from both sides.

$$4A^{2}-A^{2}=-324$$

Combine 4A^{2} and -A^{2} to get 3A^{2}.

$$3A^{2}=-324$$

Add 324 to both sides.

$$3A^{2}+324=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 324 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$A=\frac{0±\sqrt{0^{2}-4\times 3\times 324}}{2\times 3}$$

Square 0.

$$A=\frac{0±\sqrt{-4\times 3\times 324}}{2\times 3}$$

Multiply -4 times 3.

$$A=\frac{0±\sqrt{-12\times 324}}{2\times 3}$$

Multiply -12 times 324.

$$A=\frac{0±\sqrt{-3888}}{2\times 3}$$

Take the square root of -3888.

$$A=\frac{0±36\sqrt{3}i}{2\times 3}$$

Multiply 2 times 3.

$$A=\frac{0±36\sqrt{3}i}{6}$$

Now solve the equation A=\frac{0±36\sqrt{3}i}{6} when ± is plus.

$$A=6\sqrt{3}i$$

Now solve the equation A=\frac{0±36\sqrt{3}i}{6} when ± is minus.

$$A=-6\sqrt{3}i$$

The equation is now solved.

$$A=6\sqrt{3}i A=-6\sqrt{3}i$$