Solve x^2=-19

$$x ^ { 2 } = - 19$$

Solve for x (complex solution)

$$x=-\sqrt{19}i\approx -0-4.358898944i$$

$$x=\sqrt{19}i\approx 4.358898944i$$

Steps by Finding Square Root

The equation is now solved.

$$x=\sqrt{19}i x=-\sqrt{19}i$$

Steps Using the Quadratic Formula

Add 19 to both sides.

$$x^{2}+19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 19}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 19}}{2}$$

Multiply -4 times 19.

$$x=\frac{0±\sqrt{-76}}{2}$$

Take the square root of -76.

$$x=\frac{0±2\sqrt{19}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{19}i}{2} when ± is plus.

$$x=\sqrt{19}i$$

Now solve the equation x=\frac{0±2\sqrt{19}i}{2} when ± is minus.

$$x=-\sqrt{19}i$$

The equation is now solved.

$$x=\sqrt{19}i x=-\sqrt{19}i$$