Solve sqrt{5*3}+2x^2=0=

$$\sqrt{ 5 \times 3 } +2 { x }^{ 2 } =0=$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}\sqrt[4]{15}i}{2}\approx -0-1.391578842i$$

$$x=\frac{\sqrt{2}\sqrt[4]{15}i}{2}\approx 1.391578842i$$

Steps by Finding Square Root

Multiply 5 and 3 to get 15.

$$\sqrt{15}+2x^{2}=0$$

Subtract \sqrt{15} from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}=-\sqrt{15}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}=-\frac{\sqrt{15}}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{2}\sqrt[4]{15}i}{2} x=-\frac{\sqrt{2}\sqrt[4]{15}i}{2}$$

Steps Using the Quadratic Formula

Multiply 5 and 3 to get 15.

$$\sqrt{15}+2x^{2}=0$$

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.

$$2x^{2}+\sqrt{15}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and \sqrt{15} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\sqrt{15}}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\sqrt{15}}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\sqrt{15}}}{2\times 2}$$

Take the square root of -8\sqrt{15}.

$$x=\frac{0±2\sqrt{2}i\sqrt[4]{15}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{2}i\sqrt[4]{15}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{2}i\sqrt[4]{15}}{4} when ± is plus.

$$x=\frac{\sqrt{2}\sqrt[4]{15}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}i\sqrt[4]{15}}{4} when ± is minus.

$$x=-\frac{\sqrt{2}\sqrt[4]{15}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{2}\sqrt[4]{15}i}{2} x=-\frac{\sqrt{2}\sqrt[4]{15}i}{2}$$