Solve 6x^2+4=-46

$$6 x ^ { 2 } + 4 = - 46$$

Solve for x (complex solution)

$$x=-\frac{5\sqrt{3}i}{3}\approx -0-2.886751346i$$

$$x=\frac{5\sqrt{3}i}{3}\approx 2.886751346i$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$6x^{2}=-46-4$$

Subtract 4 from -46 to get -50.

$$6x^{2}=-50$$

Divide both sides by 6.

$$x^{2}=\frac{-50}{6}$$

Reduce the fraction \frac{-50}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{25}{3}$$

The equation is now solved.

$$x=\frac{5\sqrt{3}i}{3} x=-\frac{5\sqrt{3}i}{3}$$

Steps Using the Quadratic Formula

Add 46 to both sides.

$$6x^{2}+4+46=0$$

Add 4 and 46 to get 50.

$$6x^{2}+50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 50}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\times 50}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 50}}{2\times 6}$$

Multiply -24 times 50.

$$x=\frac{0±\sqrt{-1200}}{2\times 6}$$

Take the square root of -1200.

$$x=\frac{0±20\sqrt{3}i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±20\sqrt{3}i}{12}$$

Now solve the equation x=\frac{0±20\sqrt{3}i}{12} when ± is plus.

$$x=\frac{5\sqrt{3}i}{3}$$

Now solve the equation x=\frac{0±20\sqrt{3}i}{12} when ± is minus.

$$x=-\frac{5\sqrt{3}i}{3}$$

The equation is now solved.

$$x=\frac{5\sqrt{3}i}{3} x=-\frac{5\sqrt{3}i}{3}$$