Solve a^2+8=5

$$a ^ { 2 } + 8 = 5$$

Solve for a

$$a=-\sqrt{3}i\approx -0-1.732050808i$$

$$a=\sqrt{3}i\approx 1.732050808i$$

Steps by Finding Square Root

Subtract 8 from both sides.

$$a^{2}=5-8$$

Subtract 8 from 5 to get -3.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Subtract 5 from both sides.

$$a^{2}+8-5=0$$

Subtract 5 from 8 to get 3.

$$a^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

$$a=\frac{0±\sqrt{-4\times 3}}{2}$$

Multiply -4 times 3.

$$a=\frac{0±\sqrt{-12}}{2}$$

Take the square root of -12.

$$a=\frac{0±2\sqrt{3}i}{2}$$

Now solve the equation a=\frac{0±2\sqrt{3}i}{2} when ± is plus.

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

Now solve the equation a=\frac{0±2\sqrt{3}i}{2} when ± is minus.

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

The equation is now solved.

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