Solve 2x^2+24=13

$$2 x ^ { 2 } + 24 = 13$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{22}i}{2}\approx -0-2.34520788i$$

$$x=\frac{\sqrt{22}i}{2}\approx 2.34520788i$$

Steps by Finding Square Root

Subtract 24 from both sides.

$$2x^{2}=13-24$$

Subtract 24 from 13 to get -11.

$$2x^{2}=-11$$

Divide both sides by 2.

$$x^{2}=-\frac{11}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{22}i}{2} x=-\frac{\sqrt{22}i}{2}$$

Steps Using the Quadratic Formula

Subtract 13 from both sides.

$$2x^{2}+24-13=0$$

Subtract 13 from 24 to get 11.

$$2x^{2}+11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 11}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 11}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 11}}{2\times 2}$$

Multiply -8 times 11.

$$x=\frac{0±\sqrt{-88}}{2\times 2}$$

Take the square root of -88.

$$x=\frac{0±2\sqrt{22}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{22}i}{4}$$

Now solve the equation x=\frac{0±2\sqrt{22}i}{4} when ± is plus.

$$x=\frac{\sqrt{22}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{22}i}{4} when ± is minus.

$$x=-\frac{\sqrt{22}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{22}i}{2} x=-\frac{\sqrt{22}i}{2}$$