Solve 6x^2-11=-150

$$6 x ^ { 2 } - 11 = - 150$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{834}i}{6}\approx -0-4.813176359i$$

$$x=\frac{\sqrt{834}i}{6}\approx 4.813176359i$$

Steps by Finding Square Root

Add 11 to both sides.

$$6x^{2}=-150+11$$

Add -150 and 11 to get -139.

$$6x^{2}=-139$$

Divide both sides by 6.

$$x^{2}=-\frac{139}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{834}i}{6} x=-\frac{\sqrt{834}i}{6}$$

Steps Using the Quadratic Formula

Add 150 to both sides.

$$6x^{2}-11+150=0$$

Add -11 and 150 to get 139.

$$6x^{2}+139=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 139 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 139}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\times 139}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 139}}{2\times 6}$$

Multiply -24 times 139.

$$x=\frac{0±\sqrt{-3336}}{2\times 6}$$

Take the square root of -3336.

$$x=\frac{0±2\sqrt{834}i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±2\sqrt{834}i}{12}$$

Now solve the equation x=\frac{0±2\sqrt{834}i}{12} when ± is plus.

$$x=\frac{\sqrt{834}i}{6}$$

Now solve the equation x=\frac{0±2\sqrt{834}i}{12} when ± is minus.

$$x=-\frac{\sqrt{834}i}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{834}i}{6} x=-\frac{\sqrt{834}i}{6}$$