Solve a^2+625=25+41

$$a ^ { 2 } + 625 = 25 + 41$$

Solve for a

$$a=-\sqrt{559}i\approx -0-23.643180835i$$

$$a=\sqrt{559}i\approx 23.643180835i$$

Steps by Finding Square Root

Add 25 and 41 to get 66.

$$a^{2}+625=66$$

Subtract 625 from both sides.

$$a^{2}=66-625$$

Subtract 625 from 66 to get -559.

$$a^{2}=-559$$

The equation is now solved.

$$a=\sqrt{559}i a=-\sqrt{559}i$$

Steps Using the Quadratic Formula

Add 25 and 41 to get 66.

$$a^{2}+625=66$$

Subtract 66 from both sides.

$$a^{2}+625-66=0$$

Subtract 66 from 625 to get 559.

$$a^{2}+559=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 559 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 559}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 559}}{2}$$

Multiply -4 times 559.

$$a=\frac{0±\sqrt{-2236}}{2}$$

Take the square root of -2236.

$$a=\frac{0±2\sqrt{559}i}{2}$$

Now solve the equation a=\frac{0±2\sqrt{559}i}{2} when ± is plus.

$$a=\sqrt{559}i$$

Now solve the equation a=\frac{0±2\sqrt{559}i}{2} when ± is minus.

$$a=-\sqrt{559}i$$

The equation is now solved.

$$a=\sqrt{559}i a=-\sqrt{559}i$$