Solve x^2+19=-72

$${ x }^{ 2 } +19 = -72$$

Solve for x (complex solution)

$$x=-\sqrt{91}i\approx -0-9.539392014i$$

$$x=\sqrt{91}i\approx 9.539392014i$$

Steps by Finding Square Root

Subtract 19 from both sides.

$$x^{2}=-72-19$$

Subtract 19 from -72 to get -91.

$$x^{2}=-91$$

The equation is now solved.

$$x=\sqrt{91}i x=-\sqrt{91}i$$

Steps Using the Quadratic Formula

Add 72 to both sides.

$$x^{2}+19+72=0$$

Add 19 and 72 to get 91.

$$x^{2}+91=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 91 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 91}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 91}}{2}$$

Multiply -4 times 91.

$$x=\frac{0±\sqrt{-364}}{2}$$

Take the square root of -364.

$$x=\frac{0±2\sqrt{91}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{91}i}{2} when ± is plus.

$$x=\sqrt{91}i$$

Now solve the equation x=\frac{0±2\sqrt{91}i}{2} when ± is minus.

$$x=-\sqrt{91}i$$

The equation is now solved.

$$x=\sqrt{91}i x=-\sqrt{91}i$$