Solve x^2-3x*(-4x)+12=8

$$x ^ { 2 } - 3 x \cdot ( - 4 x ) + 12 = 8$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{13}i}{13}\approx -0-0.554700196i$$

$$x=\frac{2\sqrt{13}i}{13}\approx 0.554700196i$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$x^{2}-3x^{2}\left(-4\right)+12=8$$

Multiply 3 and -4 to get -12.

$$x^{2}-\left(-12x^{2}\right)+12=8$$

The opposite of -12x^{2} is 12x^{2}.

$$x^{2}+12x^{2}+12=8$$

Combine x^{2} and 12x^{2} to get 13x^{2}.

$$13x^{2}+12=8$$

Subtract 12 from both sides.

$$13x^{2}=8-12$$

Subtract 12 from 8 to get -4.

$$13x^{2}=-4$$

Divide both sides by 13.

$$x^{2}=-\frac{4}{13}$$

The equation is now solved.

$$x=\frac{2\sqrt{13}i}{13} x=-\frac{2\sqrt{13}i}{13}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$x^{2}-3x^{2}\left(-4\right)+12=8$$

Multiply 3 and -4 to get -12.

$$x^{2}-\left(-12x^{2}\right)+12=8$$

The opposite of -12x^{2} is 12x^{2}.

$$x^{2}+12x^{2}+12=8$$

Combine x^{2} and 12x^{2} to get 13x^{2}.

$$13x^{2}+12=8$$

Subtract 8 from both sides.

$$13x^{2}+12-8=0$$

Subtract 8 from 12 to get 4.

$$13x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 13 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13\times 4}}{2\times 13}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13\times 4}}{2\times 13}$$

Multiply -4 times 13.

$$x=\frac{0±\sqrt{-52\times 4}}{2\times 13}$$

Multiply -52 times 4.

$$x=\frac{0±\sqrt{-208}}{2\times 13}$$

Take the square root of -208.

$$x=\frac{0±4\sqrt{13}i}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{0±4\sqrt{13}i}{26}$$

Now solve the equation x=\frac{0±4\sqrt{13}i}{26} when ± is plus.

$$x=\frac{2\sqrt{13}i}{13}$$

Now solve the equation x=\frac{0±4\sqrt{13}i}{26} when ± is minus.

$$x=-\frac{2\sqrt{13}i}{13}$$

The equation is now solved.

$$x=\frac{2\sqrt{13}i}{13} x=-\frac{2\sqrt{13}i}{13}$$