Solve 3x^2-5=-446

$$3 x ^ { 2 } - 5 = - 446$$

Solve for x (complex solution)

$$x=-7\sqrt{3}i\approx -0-12.124355653i$$

$$x=7\sqrt{3}i\approx 12.124355653i$$

Steps by Finding Square Root

Add 5 to both sides.

$$3x^{2}=-446+5$$

Add -446 and 5 to get -441.

$$3x^{2}=-441$$

Divide both sides by 3.

$$x^{2}=\frac{-441}{3}$$

Divide -441 by 3 to get -147.

$$x^{2}=-147$$

The equation is now solved.

$$x=7\sqrt{3}i x=-7\sqrt{3}i$$

Steps Using the Quadratic Formula

Add 446 to both sides.

$$3x^{2}-5+446=0$$

Add -5 and 446 to get 441.

$$3x^{2}+441=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 441 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 441}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 441}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 441}}{2\times 3}$$

Multiply -12 times 441.

$$x=\frac{0±\sqrt{-5292}}{2\times 3}$$

Take the square root of -5292.

$$x=\frac{0±42\sqrt{3}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±42\sqrt{3}i}{6}$$

Now solve the equation x=\frac{0±42\sqrt{3}i}{6} when ± is plus.

$$x=7\sqrt{3}i$$

Now solve the equation x=\frac{0±42\sqrt{3}i}{6} when ± is minus.

$$x=-7\sqrt{3}i$$

The equation is now solved.

$$x=7\sqrt{3}i x=-7\sqrt{3}i$$