Solve -3^2=a^2

$$- 3 ^ { 2 } = a ^ { 2 }$$

Solve for a

$$a=3i$$

$$a=-3i$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$-9=a^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}=-9$$

The equation is now solved.

$$a=3i a=-3i$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$-9=a^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$a^{2}=-9$$

Add 9 to both sides.

$$a^{2}+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 9}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 9}}{2}$$

Multiply -4 times 9.

$$a=\frac{0±\sqrt{-36}}{2}$$

Take the square root of -36.

$$a=\frac{0±6i}{2}$$

Now solve the equation a=\frac{0±6i}{2} when ± is plus.

$$a=3i$$

Now solve the equation a=\frac{0±6i}{2} when ± is minus.

$$a=-3i$$

The equation is now solved.

$$a=3i a=-3i$$