Solve x^2+15=0

$${ x }^{ 2 } +15=0$$

Solve for x (complex solution)

$$x=-\sqrt{15}i\approx -0-3.872983346i$$

$$x=\sqrt{15}i\approx 3.872983346i$$

Steps by Finding Square Root

Subtract 15 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-15$$

The equation is now solved.

$$x=\sqrt{15}i x=-\sqrt{15}i$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}+15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 15}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 15}}{2}$$

Multiply -4 times 15.

$$x=\frac{0±\sqrt{-60}}{2}$$

Take the square root of -60.

$$x=\frac{0±2\sqrt{15}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{15}i}{2} when ± is plus.

$$x=\sqrt{15}i$$

Now solve the equation x=\frac{0±2\sqrt{15}i}{2} when ± is minus.

$$x=-\sqrt{15}i$$

The equation is now solved.

$$x=\sqrt{15}i x=-\sqrt{15}i$$