Solve 2x^2+57/x=0

$$\frac { 2 x ^ { 2 } + 57 } { x } = 0$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{114}i}{2}\approx -0-5.338539126i$$

$$x=\frac{\sqrt{114}i}{2}\approx 5.338539126i$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$2x^{2}+57=0$$

Subtract 57 from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}=-57$$

Divide both sides by 2.

$$x^{2}=-\frac{57}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{114}i}{2} x=-\frac{\sqrt{114}i}{2}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$2x^{2}+57=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 57 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 57}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 57}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 57}}{2\times 2}$$

Multiply -8 times 57.

$$x=\frac{0±\sqrt{-456}}{2\times 2}$$

Take the square root of -456.

$$x=\frac{0±2\sqrt{114}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{114}i}{4}$$

Now solve the equation x=\frac{0±2\sqrt{114}i}{4} when ± is plus.

$$x=\frac{\sqrt{114}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{114}i}{4} when ± is minus.

$$x=-\frac{\sqrt{114}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{114}i}{2} x=-\frac{\sqrt{114}i}{2}$$