Solve 2x^2-16x^2=x^2+18

$$2 { x }^{ 2 } -16 { x }^{ 2 } = { x }^{ 2 } +18$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{30}i}{5}\approx -0-1.095445115i$$

$$x=\frac{\sqrt{30}i}{5}\approx 1.095445115i$$

Steps by Finding Square Root

Combine 2x^{2} and -16x^{2} to get -14x^{2}.

$$-14x^{2}=x^{2}+18$$

Subtract x^{2} from both sides.

$$-14x^{2}-x^{2}=18$$

Combine -14x^{2} and -x^{2} to get -15x^{2}.

$$-15x^{2}=18$$

Divide both sides by -15.

$$x^{2}=\frac{18}{-15}$$

Reduce the fraction \frac{18}{-15} to lowest terms by extracting and canceling out 3.

$$x^{2}=-\frac{6}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{30}i}{5} x=-\frac{\sqrt{30}i}{5}$$

Steps Using the Quadratic Formula

Combine 2x^{2} and -16x^{2} to get -14x^{2}.

$$-14x^{2}=x^{2}+18$$

Subtract x^{2} from both sides.

$$-14x^{2}-x^{2}=18$$

Combine -14x^{2} and -x^{2} to get -15x^{2}.

$$-15x^{2}=18$$

Subtract 18 from both sides.

$$-15x^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -15 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\left(-18\right)}}{2\left(-15\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\left(-18\right)}}{2\left(-15\right)}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60\left(-18\right)}}{2\left(-15\right)}$$

Multiply 60 times -18.

$$x=\frac{0±\sqrt{-1080}}{2\left(-15\right)}$$

Take the square root of -1080.

$$x=\frac{0±6\sqrt{30}i}{2\left(-15\right)}$$

Multiply 2 times -15.

$$x=\frac{0±6\sqrt{30}i}{-30}$$

Now solve the equation x=\frac{0±6\sqrt{30}i}{-30} when ± is plus.

$$x=-\frac{\sqrt{30}i}{5}$$

Now solve the equation x=\frac{0±6\sqrt{30}i}{-30} when ± is minus.

$$x=\frac{\sqrt{30}i}{5}$$

The equation is now solved.

$$x=-\frac{\sqrt{30}i}{5} x=\frac{\sqrt{30}i}{5}$$