Solve 0=2(x^2+14-3)

$$0 = 2 ( x ^ { 2 } + 14 - 3 )$$

Solve for x (complex solution)

$$x=-\sqrt{11}i\approx -0-3.31662479i$$

$$x=\sqrt{11}i\approx 3.31662479i$$

Steps by Finding Square Root

Divide both sides by 2. Zero divided by any non-zero number gives zero.

$$0=x^{2}+14-3$$

Subtract 3 from 14 to get 11.

$$0=x^{2}+11$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+11=0$$

Subtract 11 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-11$$

The equation is now solved.

$$x=\sqrt{11}i x=-\sqrt{11}i$$

Steps Using the Quadratic Formula

Divide both sides by 2. Zero divided by any non-zero number gives zero.

$$0=x^{2}+14-3$$

Subtract 3 from 14 to get 11.

$$0=x^{2}+11$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11}}{2}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44}}{2}$$

Take the square root of -44.

$$x=\frac{0±2\sqrt{11}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{11}i}{2} when ± is plus.

$$x=\sqrt{11}i$$

Now solve the equation x=\frac{0±2\sqrt{11}i}{2} when ± is minus.

$$x=-\sqrt{11}i$$

The equation is now solved.

$$x=\sqrt{11}i x=-\sqrt{11}i$$