Solve -3x^2-75=0

$$- 3 x ^ { 2 } - 75 = 0$$

Solve for x (complex solution)

$$x=-5i$$

$$x=5i$$

Steps by Finding Square Root

Add 75 to both sides. Anything plus zero gives itself.

$$-3x^{2}=75$$

Divide both sides by -3.

$$x^{2}=\frac{75}{-3}$$

Divide 75 by -3 to get -25.

$$x^{2}=-25$$

The equation is now solved.

$$x=5i x=-5i$$

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.

$$-3x^{2}-75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and -75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\left(-75\right)}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\left(-75\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\left(-75\right)}}{2\left(-3\right)}$$

Multiply 12 times -75.

$$x=\frac{0±\sqrt{-900}}{2\left(-3\right)}$$

Take the square root of -900.

$$x=\frac{0±30i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±30i}{-6}$$

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

$$x=-5i$$

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

$$x=5i$$

The equation is now solved.

$$x=-5i x=5i$$