Solve 27=x^2-12x^2+4

$$27 = x ^ { 2 } - 12 x ^ { 2 } + 4$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{253}i}{11}\approx -0-1.445997611i$$

$$x=\frac{\sqrt{253}i}{11}\approx 1.445997611i$$

Steps by Finding Square Root

Combine x^{2} and -12x^{2} to get -11x^{2}.

$$27=-11x^{2}+4$$

Swap sides so that all variable terms are on the left hand side.

$$-11x^{2}+4=27$$

Subtract 4 from both sides.

$$-11x^{2}=27-4$$

Subtract 4 from 27 to get 23.

$$-11x^{2}=23$$

Divide both sides by -11.

$$x^{2}=-\frac{23}{11}$$

The equation is now solved.

$$x=\frac{\sqrt{253}i}{11} x=-\frac{\sqrt{253}i}{11}$$

Steps Using the Quadratic Formula

Combine x^{2} and -12x^{2} to get -11x^{2}.

$$27=-11x^{2}+4$$

Swap sides so that all variable terms are on the left hand side.

$$-11x^{2}+4=27$$

Subtract 27 from both sides.

$$-11x^{2}+4-27=0$$

Subtract 27 from 4 to get -23.

$$-11x^{2}-23=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -11 for a, 0 for b, and -23 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-11\right)\left(-23\right)}}{2\left(-11\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-11\right)\left(-23\right)}}{2\left(-11\right)}$$

Multiply -4 times -11.

$$x=\frac{0±\sqrt{44\left(-23\right)}}{2\left(-11\right)}$$

Multiply 44 times -23.

$$x=\frac{0±\sqrt{-1012}}{2\left(-11\right)}$$

Take the square root of -1012.

$$x=\frac{0±2\sqrt{253}i}{2\left(-11\right)}$$

Multiply 2 times -11.

$$x=\frac{0±2\sqrt{253}i}{-22}$$

Now solve the equation x=\frac{0±2\sqrt{253}i}{-22} when ± is plus.

$$x=-\frac{\sqrt{253}i}{11}$$

Now solve the equation x=\frac{0±2\sqrt{253}i}{-22} when ± is minus.

$$x=\frac{\sqrt{253}i}{11}$$

The equation is now solved.

$$x=-\frac{\sqrt{253}i}{11} x=\frac{\sqrt{253}i}{11}$$