Solve 2x^2-5=-19

$$2 x ^ { 2 } - 5 = - 19$$

Solve for x (complex solution)

$$x=-\sqrt{7}i\approx -0-2.645751311i$$

$$x=\sqrt{7}i\approx 2.645751311i$$

Steps by Finding Square Root

Add 5 to both sides.

$$2x^{2}=-19+5$$

Add -19 and 5 to get -14.

$$2x^{2}=-14$$

Divide both sides by 2.

$$x^{2}=\frac{-14}{2}$$

Divide -14 by 2 to get -7.

$$x^{2}=-7$$

The equation is now solved.

$$x=\sqrt{7}i x=-\sqrt{7}i$$

Steps Using the Quadratic Formula

Add 19 to both sides.

$$2x^{2}-5+19=0$$

Add -5 and 19 to get 14.

$$2x^{2}+14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 14}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 14}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 14}}{2\times 2}$$

Multiply -8 times 14.

$$x=\frac{0±\sqrt{-112}}{2\times 2}$$

Take the square root of -112.

$$x=\frac{0±4\sqrt{7}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{7}i}{4}$$

Now solve the equation x=\frac{0±4\sqrt{7}i}{4} when ± is plus.

$$x=\sqrt{7}i$$

Now solve the equation x=\frac{0±4\sqrt{7}i}{4} when ± is minus.

$$x=-\sqrt{7}i$$

The equation is now solved.

$$x=\sqrt{7}i x=-\sqrt{7}i$$