Solve 8x^2+32=0

$$8 { x }^{ 2 } +32=0$$

Solve for x (complex solution)

$$x=-2i$$

$$x=2i$$

Steps by Finding Square Root

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

$$8x^{2}=-32$$

Divide both sides by 8.

$$x^{2}=\frac{-32}{8}$$

Divide -32 by 8 to get -4.

$$x^{2}=-4$$

The equation is now solved.

$$x=2i x=-2i$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$8x^{2}+32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and 32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\times 32}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\times 32}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\times 32}}{2\times 8}$$

Multiply -32 times 32.

$$x=\frac{0±\sqrt{-1024}}{2\times 8}$$

Take the square root of -1024.

$$x=\frac{0±32i}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±32i}{16}$$

Now solve the equation x=\frac{0±32i}{16} when ± is plus.

$$x=2i$$

Now solve the equation x=\frac{0±32i}{16} when ± is minus.

$$x=-2i$$

The equation is now solved.

$$x=2i x=-2i$$