Solve -2/3x^2-1=17

$$- \frac { 2 } { 3 } x ^ { 2 } - 1 = 17$$

Solve for x (complex solution)

$$x=-3\sqrt{3}i\approx -0-5.196152423i$$

$$x=3\sqrt{3}i\approx 5.196152423i$$

Steps by Finding Square Root

Add 1 to both sides.

$$-\frac{2}{3}x^{2}=17+1$$

Add 17 and 1 to get 18.

$$-\frac{2}{3}x^{2}=18$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$x^{2}=18\left(-\frac{3}{2}\right)$$

Multiply 18 and -\frac{3}{2} to get -27.

$$x^{2}=-27$$

The equation is now solved.

$$x=3\sqrt{3}i x=-3\sqrt{3}i$$

Steps Using the Quadratic Formula

Subtract 17 from both sides.

$$-\frac{2}{3}x^{2}-1-17=0$$

Subtract 17 from -1 to get -18.

$$-\frac{2}{3}x^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{2}{3} for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{2}{3}\right)\left(-18\right)}}{2\left(-\frac{2}{3}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{2}{3}\right)\left(-18\right)}}{2\left(-\frac{2}{3}\right)}$$

Multiply -4 times -\frac{2}{3}.

$$x=\frac{0±\sqrt{\frac{8}{3}\left(-18\right)}}{2\left(-\frac{2}{3}\right)}$$

Multiply \frac{8}{3} times -18.

$$x=\frac{0±\sqrt{-48}}{2\left(-\frac{2}{3}\right)}$$

Take the square root of -48.

$$x=\frac{0±4\sqrt{3}i}{2\left(-\frac{2}{3}\right)}$$

Multiply 2 times -\frac{2}{3}.

$$x=\frac{0±4\sqrt{3}i}{-\frac{4}{3}}$$

Now solve the equation x=\frac{0±4\sqrt{3}i}{-\frac{4}{3}} when ± is plus.

$$x=-3\sqrt{3}i$$

Now solve the equation x=\frac{0±4\sqrt{3}i}{-\frac{4}{3}} when ± is minus.

$$x=3\sqrt{3}i$$

The equation is now solved.

$$x=-3\sqrt{3}i x=3\sqrt{3}i$$