Solve x^2-72+182=0

$$x ^ { 2 } - 72 + 182 = 0$$

Solve for x (complex solution)

$$x=-\sqrt{110}i\approx -0-10.488088482i$$

$$x=\sqrt{110}i\approx 10.488088482i$$

Steps by Finding Square Root

Add -72 and 182 to get 110.

$$x^{2}+110=0$$

Subtract 110 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-110$$

The equation is now solved.

$$x=\sqrt{110}i x=-\sqrt{110}i$$

Steps Using the Quadratic Formula

Add -72 and 182 to get 110.

$$x^{2}+110=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 110 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 110}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 110}}{2}$$

Multiply -4 times 110.

$$x=\frac{0±\sqrt{-440}}{2}$$

Take the square root of -440.

$$x=\frac{0±2\sqrt{110}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{110}i}{2} when ± is plus.

$$x=\sqrt{110}i$$

Now solve the equation x=\frac{0±2\sqrt{110}i}{2} when ± is minus.

$$x=-\sqrt{110}i$$

The equation is now solved.

$$x=\sqrt{110}i x=-\sqrt{110}i$$