Solve 6x^2+150=0

$$6 x ^ { 2 } + 150 = 0$$

Solve for x (complex solution)

$$x=-5i$$

$$x=5i$$

Steps by Finding Square Root

Subtract 150 from both sides. Anything subtracted from zero gives its negation.

$$6x^{2}=-150$$

Divide both sides by 6.

$$x^{2}=\frac{-150}{6}$$

Divide -150 by 6 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.

$$6x^{2}+150=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 150 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 150}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\times 150}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 150}}{2\times 6}$$

Multiply -24 times 150.

$$x=\frac{0±\sqrt{-3600}}{2\times 6}$$

Take the square root of -3600.

$$x=\frac{0±60i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±60i}{12}$$

Now solve the equation x=\frac{0±60i}{12} when ± is plus.

$$x=5i$$

Now solve the equation x=\frac{0±60i}{12} when ± is minus.

$$x=-5i$$

The equation is now solved.

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