Solve x^2-12+125=90

$${ x }^{ 2 } -12+125=90$$

Solve for x (complex solution)

$$x=-\sqrt{23}i\approx -0-4.795831523i$$

$$x=\sqrt{23}i\approx 4.795831523i$$

Steps by Finding Square Root

Add -12 and 125 to get 113.

$$x^{2}+113=90$$

Subtract 113 from both sides.

$$x^{2}=90-113$$

Subtract 113 from 90 to get -23.

$$x^{2}=-23$$

The equation is now solved.

$$x=\sqrt{23}i x=-\sqrt{23}i$$

Steps Using the Quadratic Formula

Add -12 and 125 to get 113.

$$x^{2}+113=90$$

Subtract 90 from both sides.

$$x^{2}+113-90=0$$

Subtract 90 from 113 to get 23.

$$x^{2}+23=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 23 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 23}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 23}}{2}$$

Multiply -4 times 23.

$$x=\frac{0±\sqrt{-92}}{2}$$

Take the square root of -92.

$$x=\frac{0±2\sqrt{23}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{23}i}{2} when ± is plus.

$$x=\sqrt{23}i$$

Now solve the equation x=\frac{0±2\sqrt{23}i}{2} when ± is minus.

$$x=-\sqrt{23}i$$

The equation is now solved.

$$x=\sqrt{23}i x=-\sqrt{23}i$$