Solve a^2+23^2=15^2

$$a ^ { 2 } + 23 ^ { 2 } = 15 ^ { 2 }$$

Solve for a

$$a=-4\sqrt{19}i\approx -0-17.435595774i$$

$$a=4\sqrt{19}i\approx 17.435595774i$$

Steps by Finding Square Root

Calculate 23 to the power of 2 and get 529.

$$a^{2}+529=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$a^{2}+529=225$$

Subtract 529 from both sides.

$$a^{2}=225-529$$

Subtract 529 from 225 to get -304.

$$a^{2}=-304$$

The equation is now solved.

$$a=4\sqrt{19}i a=-4\sqrt{19}i$$

Steps Using the Quadratic Formula

Calculate 23 to the power of 2 and get 529.

$$a^{2}+529=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$a^{2}+529=225$$

Subtract 225 from both sides.

$$a^{2}+529-225=0$$

Subtract 225 from 529 to get 304.

$$a^{2}+304=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 304 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 304}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 304}}{2}$$

Multiply -4 times 304.

$$a=\frac{0±\sqrt{-1216}}{2}$$

Take the square root of -1216.

$$a=\frac{0±8\sqrt{19}i}{2}$$

Now solve the equation a=\frac{0±8\sqrt{19}i}{2} when ± is plus.

$$a=4\sqrt{19}i$$

Now solve the equation a=\frac{0±8\sqrt{19}i}{2} when ± is minus.

$$a=-4\sqrt{19}i$$

The equation is now solved.

$$a=4\sqrt{19}i a=-4\sqrt{19}i$$