Solve x^2+30+2=0

$${ x }^{ 2 } +30+2=0$$

Solve for x (complex solution)

$$x=-4\sqrt{2}i\approx -0-5.656854249i$$

$$x=4\sqrt{2}i\approx 5.656854249i$$

Steps by Finding Square Root

Add 30 and 2 to get 32.

$$x^{2}+32=0$$

Subtract 32 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-32$$

The equation is now solved.

$$x=4\sqrt{2}i x=-4\sqrt{2}i$$

Steps Using the Quadratic Formula

Add 30 and 2 to get 32.

$$x^{2}+32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 32}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 32}}{2}$$

Multiply -4 times 32.

$$x=\frac{0±\sqrt{-128}}{2}$$

Take the square root of -128.

$$x=\frac{0±8\sqrt{2}i}{2}$$

Now solve the equation x=\frac{0±8\sqrt{2}i}{2} when ± is plus.

$$x=4\sqrt{2}i$$

Now solve the equation x=\frac{0±8\sqrt{2}i}{2} when ± is minus.

$$x=-4\sqrt{2}i$$

The equation is now solved.

$$x=4\sqrt{2}i x=-4\sqrt{2}i$$