Solve x^2=-54

$$x ^ { 2 } = - 54$$

Solve for x (complex solution)

$$x=-3\sqrt{6}i\approx -0-7.348469228i$$

$$x=3\sqrt{6}i\approx 7.348469228i$$

Steps by Finding Square Root

The equation is now solved.

$$x=3\sqrt{6}i x=-3\sqrt{6}i$$

Steps Using the Quadratic Formula

Add 54 to both sides.

$$x^{2}+54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 54}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 54}}{2}$$

Multiply -4 times 54.

$$x=\frac{0±\sqrt{-216}}{2}$$

Take the square root of -216.

$$x=\frac{0±6\sqrt{6}i}{2}$$

Now solve the equation x=\frac{0±6\sqrt{6}i}{2} when ± is plus.

$$x=3\sqrt{6}i$$

Now solve the equation x=\frac{0±6\sqrt{6}i}{2} when ± is minus.

$$x=-3\sqrt{6}i$$

The equation is now solved.

$$x=3\sqrt{6}i x=-3\sqrt{6}i$$