Solve -3x^2-867=0

$$- 3 x ^ { 2 } - 867 = 0$$

Solve for x (complex solution)

$$x=-17i$$

$$x=17i$$

Steps by Finding Square Root

Add 867 to both sides. Anything plus zero gives itself.

$$-3x^{2}=867$$

Divide both sides by -3.

$$x^{2}=\frac{867}{-3}$$

Divide 867 by -3 to get -289.

$$x^{2}=-289$$

The equation is now solved.

$$x=17i x=-17i$$

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.

$$-3x^{2}-867=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and -867 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\left(-867\right)}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\left(-867\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\left(-867\right)}}{2\left(-3\right)}$$

Multiply 12 times -867.

$$x=\frac{0±\sqrt{-10404}}{2\left(-3\right)}$$

Take the square root of -10404.

$$x=\frac{0±102i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±102i}{-6}$$

Now solve the equation x=\frac{0±102i}{-6} when ± is plus.

$$x=-17i$$

Now solve the equation x=\frac{0±102i}{-6} when ± is minus.

$$x=17i$$

The equation is now solved.

$$x=-17i x=17i$$