Solve x^2+55-13=0

$${ x }^{ 2 } +55-13=0$$

Solve for x (complex solution)

$$x=-\sqrt{42}i\approx -0-6.480740698i$$

$$x=\sqrt{42}i\approx 6.480740698i$$

Steps by Finding Square Root

Subtract 13 from 55 to get 42.

$$x^{2}+42=0$$

Subtract 42 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-42$$

The equation is now solved.

$$x=\sqrt{42}i x=-\sqrt{42}i$$

Steps Using the Quadratic Formula

Subtract 13 from 55 to get 42.

$$x^{2}+42=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 42 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 42}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 42}}{2}$$

Multiply -4 times 42.

$$x=\frac{0±\sqrt{-168}}{2}$$

Take the square root of -168.

$$x=\frac{0±2\sqrt{42}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{42}i}{2} when ± is plus.

$$x=\sqrt{42}i$$

Now solve the equation x=\frac{0±2\sqrt{42}i}{2} when ± is minus.

$$x=-\sqrt{42}i$$

The equation is now solved.

$$x=\sqrt{42}i x=-\sqrt{42}i$$