Solve 2a^2+18=0

$$2 a ^ { 2 } + 18 = 0$$

Solve for a

$$a=-3i$$

$$a=3i$$

Steps by Finding Square Root

Subtract 18 from both sides. Anything subtracted from zero gives its negation.

$$2a^{2}=-18$$

Divide both sides by 2.

$$a^{2}=\frac{-18}{2}$$

Divide -18 by 2 to get -9.

$$a^{2}=-9$$

The equation is now solved.

$$a=3i a=-3i$$

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.

$$2a^{2}+18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 2\times 18}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\times 18}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\times 18}}{2\times 2}$$

Multiply -8 times 18.

$$a=\frac{0±\sqrt{-144}}{2\times 2}$$

Take the square root of -144.

$$a=\frac{0±12i}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±12i}{4}$$

Now solve the equation a=\frac{0±12i}{4} when ± is plus.

$$a=3i$$

Now solve the equation a=\frac{0±12i}{4} when ± is minus.

$$a=-3i$$

The equation is now solved.

$$a=3i a=-3i$$