Solve x^2+10+8+120=0

$${ x }^{ 2 } +10+8+120=0$$

Solve for x (complex solution)

$$x=-\sqrt{138}i\approx -0-11.747340124i$$

$$x=\sqrt{138}i\approx 11.747340124i$$

Steps by Finding Square Root

Add 10 and 8 to get 18.

$$x^{2}+18+120=0$$

Add 18 and 120 to get 138.

$$x^{2}+138=0$$

Subtract 138 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-138$$

The equation is now solved.

$$x=\sqrt{138}i x=-\sqrt{138}i$$

Steps Using the Quadratic Formula

Add 10 and 8 to get 18.

$$x^{2}+18+120=0$$

Add 18 and 120 to get 138.

$$x^{2}+138=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 138 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 138}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 138}}{2}$$

Multiply -4 times 138.

$$x=\frac{0±\sqrt{-552}}{2}$$

Take the square root of -552.

$$x=\frac{0±2\sqrt{138}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{138}i}{2} when ± is plus.

$$x=\sqrt{138}i$$

Now solve the equation x=\frac{0±2\sqrt{138}i}{2} when ± is minus.

$$x=-\sqrt{138}i$$

The equation is now solved.

$$x=\sqrt{138}i x=-\sqrt{138}i$$