Solve -4x^2-27-18=0

$$-4 { x }^{ 2 } -27-18 = 0$$

Solve for x (complex solution)

$$x=-\frac{3\sqrt{5}i}{2}\approx -0-3.354101966i$$

$$x=\frac{3\sqrt{5}i}{2}\approx 3.354101966i$$

Steps by Finding Square Root

Subtract 18 from -27 to get -45.

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

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

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

Divide both sides by -4.

$$x^{2}=-\frac{45}{4}$$

The equation is now solved.

$$x=\frac{3\sqrt{5}i}{2} x=-\frac{3\sqrt{5}i}{2}$$

Steps Using the Quadratic Formula

Subtract 18 from -27 to get -45.

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

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

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

Square 0.

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

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\left(-45\right)}}{2\left(-4\right)}$$

Multiply 16 times -45.

$$x=\frac{0±\sqrt{-720}}{2\left(-4\right)}$$

Take the square root of -720.

$$x=\frac{0±12\sqrt{5}i}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±12\sqrt{5}i}{-8}$$

Now solve the equation x=\frac{0±12\sqrt{5}i}{-8} when ± is plus.

$$x=-\frac{3\sqrt{5}i}{2}$$

Now solve the equation x=\frac{0±12\sqrt{5}i}{-8} when ± is minus.

$$x=\frac{3\sqrt{5}i}{2}$$

The equation is now solved.

$$x=-\frac{3\sqrt{5}i}{2} x=\frac{3\sqrt{5}i}{2}$$