Solve 2z^2+12=0

$$2 { z }^{ 2 } +12=0$$

Solve for z

$$z=-\sqrt{6}i\approx -0-2.449489743i$$

$$z=\sqrt{6}i\approx 2.449489743i$$

Steps by Finding Square Root

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$2z^{2}=-12$$

Divide both sides by 2.

$$z^{2}=\frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$z^{2}=-6$$

The equation is now solved.

$$z=\sqrt{6}i z=-\sqrt{6}i$$

Steps Using the Quadratic Formula

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.

$$2z^{2}+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 2\times 12}}{2\times 2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 2\times 12}}{2\times 2}$$

Multiply -4 times 2.

$$z=\frac{0±\sqrt{-8\times 12}}{2\times 2}$$

Multiply -8 times 12.

$$z=\frac{0±\sqrt{-96}}{2\times 2}$$

Take the square root of -96.

$$z=\frac{0±4\sqrt{6}i}{2\times 2}$$

Multiply 2 times 2.

$$z=\frac{0±4\sqrt{6}i}{4}$$

Now solve the equation z=\frac{0±4\sqrt{6}i}{4} when ± is plus.

$$z=\sqrt{6}i$$

Now solve the equation z=\frac{0±4\sqrt{6}i}{4} when ± is minus.

$$z=-\sqrt{6}i$$

The equation is now solved.

$$z=\sqrt{6}i z=-\sqrt{6}i$$