Solve a^2=15^2-18^2

$$a ^ { 2 } = 15 ^ { 2 } - 18 ^ { 2 }$$

Solve for a

$$a=-3\sqrt{11}i\approx -0-9.949874371i$$

$$a=3\sqrt{11}i\approx 9.949874371i$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$a^{2}=225-18^{2}$$

Calculate 18 to the power of 2 and get 324.

$$a^{2}=225-324$$

Subtract 324 from 225 to get -99.

$$a^{2}=-99$$

The equation is now solved.

$$a=3\sqrt{11}i a=-3\sqrt{11}i$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$a^{2}=225-18^{2}$$

Calculate 18 to the power of 2 and get 324.

$$a^{2}=225-324$$

Subtract 324 from 225 to get -99.

$$a^{2}=-99$$

Add 99 to both sides.

$$a^{2}+99=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 99 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 99}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 99}}{2}$$

Multiply -4 times 99.

$$a=\frac{0±\sqrt{-396}}{2}$$

Take the square root of -396.

$$a=\frac{0±6\sqrt{11}i}{2}$$

Now solve the equation a=\frac{0±6\sqrt{11}i}{2} when ± is plus.

$$a=3\sqrt{11}i$$

Now solve the equation a=\frac{0±6\sqrt{11}i}{2} when ± is minus.

$$a=-3\sqrt{11}i$$

The equation is now solved.

$$a=3\sqrt{11}i a=-3\sqrt{11}i$$