Solve |sqrt[3]{-8}|+0.5x^2=0

$$| \sqrt[ 3 ] { - 8 } | + 0.5 x ^ { 2 } = 0$$

Solve for x (complex solution)

$$x=-2i$$

$$x=2i$$

Steps by Finding Square Root

Subtract |\sqrt[3]{-8}| from both sides. Anything subtracted from zero gives its negation.

$$0.5x^{2}=-|\sqrt[3]{-8}|$$

Dividing by 0.5 undoes the multiplication by 0.5.

$$x^{2}=-\frac{2}{0.5}$$

Divide -2 by 0.5 by multiplying -2 by the reciprocal of 0.5.

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

Take the square root of both sides of the equation.

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

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.

$$0.5x^{2}+|\sqrt[3]{-8}|=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.5 for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.5\times 2}}{2\times 0.5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.5\times 2}}{2\times 0.5}$$

Multiply -4 times 0.5.

$$x=\frac{0±\sqrt{-2\times 2}}{2\times 0.5}$$

Multiply -2 times 2.

$$x=\frac{0±\sqrt{-4}}{2\times 0.5}$$

Take the square root of -4.

$$x=\frac{0±2i}{2\times 0.5}$$

Multiply 2 times 0.5.

$$x=\frac{0±2i}{1}$$

Now solve the equation x=\frac{0±2i}{1} when ± is plus.

$$x=2i$$

Now solve the equation x=\frac{0±2i}{1} when ± is minus.

$$x=-2i$$

The equation is now solved.

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