Solve 3x^2+27=5

$$3 x ^ { 2 } + 27 = 5$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{66}i}{3}\approx -0-2.708012802i$$

$$x=\frac{\sqrt{66}i}{3}\approx 2.708012802i$$

Steps by Finding Square Root

Subtract 27 from both sides.

$$3x^{2}=5-27$$

Subtract 27 from 5 to get -22.

$$3x^{2}=-22$$

Divide both sides by 3.

$$x^{2}=-\frac{22}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{66}i}{3} x=-\frac{\sqrt{66}i}{3}$$

Steps Using the Quadratic Formula

Subtract 5 from both sides.

$$3x^{2}+27-5=0$$

Subtract 5 from 27 to get 22.

$$3x^{2}+22=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 22 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 22}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\times 22}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\times 22}}{2\times 3}$$

Multiply -12 times 22.

$$x=\frac{0±\sqrt{-264}}{2\times 3}$$

Take the square root of -264.

$$x=\frac{0±2\sqrt{66}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{66}i}{6}$$

Now solve the equation x=\frac{0±2\sqrt{66}i}{6} when ± is plus.

$$x=\frac{\sqrt{66}i}{3}$$

Now solve the equation x=\frac{0±2\sqrt{66}i}{6} when ± is minus.

$$x=-\frac{\sqrt{66}i}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{66}i}{3} x=-\frac{\sqrt{66}i}{3}$$