Solve x^2+36=0

$${ x }^{ 2 } +36 = 0$$

Solve for x (complex solution)

$$x=-6i$$

$$x=6i$$

Steps by Finding Square Root

Subtract 36 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-36$$

The equation is now solved.

$$x=6i x=-6i$$

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.

$$x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 36}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 36}}{2}$$

Multiply -4 times 36.

$$x=\frac{0±\sqrt{-144}}{2}$$

Take the square root of -144.

$$x=\frac{0±12i}{2}$$

Now solve the equation x=\frac{0±12i}{2} when ± is plus.

$$x=6i$$

Now solve the equation x=\frac{0±12i}{2} when ± is minus.

$$x=-6i$$

The equation is now solved.

$$x=6i x=-6i$$