Solve x^2-4x^2-45=0

$$x ^ { 2 } - 4 x ^ { 2 } - 45 = 0$$

Solve for x (complex solution)

$$x=-\sqrt{15}i\approx -0-3.872983346i$$

$$x=\sqrt{15}i\approx 3.872983346i$$

Steps by Finding Square Root

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}-45=0$$

Add 45 to both sides. Anything plus zero gives itself.

$$-3x^{2}=45$$

Divide both sides by -3.

$$x^{2}=\frac{45}{-3}$$

Divide 45 by -3 to get -15.

$$x^{2}=-15$$

The equation is now solved.

$$x=\sqrt{15}i x=-\sqrt{15}i$$

Steps Using the Quadratic Formula

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\left(-45\right)}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\left(-45\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\left(-45\right)}}{2\left(-3\right)}$$

Multiply 12 times -45.

$$x=\frac{0±\sqrt{-540}}{2\left(-3\right)}$$

Take the square root of -540.

$$x=\frac{0±6\sqrt{15}i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±6\sqrt{15}i}{-6}$$

Now solve the equation x=\frac{0±6\sqrt{15}i}{-6} when ± is plus.

$$x=-\sqrt{15}i$$

Now solve the equation x=\frac{0±6\sqrt{15}i}{-6} when ± is minus.

$$x=\sqrt{15}i$$

The equation is now solved.

$$x=-\sqrt{15}i x=\sqrt{15}i$$