Solve 2x^2+5+3=0

$$2 x ^ { 2 } + 5 + 3 = 0$$

Solve for x (complex solution)

$$x=-2i$$

$$x=2i$$

Steps by Finding Square Root

Add 5 and 3 to get 8.

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

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by 2.

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

Divide -8 by 2 to get -4.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Add 5 and 3 to get 8.

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

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

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

Square 0.

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

Multiply -4 times 2.

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

Multiply -8 times 8.

$$x=\frac{0±\sqrt{-64}}{2\times 2}$$

Take the square root of -64.

$$x=\frac{0±8i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8i}{4}$$

Now solve the equation x=\frac{0±8i}{4} when ± is plus.

$$x=2i$$

Now solve the equation x=\frac{0±8i}{4} when ± is minus.

$$x=-2i$$

The equation is now solved.

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