Solve 3x^2+9=8

$$3 x ^ { 2 } + 9 = 8$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3}i}{3}\approx -0-0.577350269i$$

$$x=\frac{\sqrt{3}i}{3}\approx 0.577350269i$$

Steps by Finding Square Root

Subtract 9 from both sides.

$$3x^{2}=8-9$$

Subtract 9 from 8 to get -1.

$$3x^{2}=-1$$

Divide both sides by 3.

$$x^{2}=-\frac{1}{3}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$3x^{2}+9-8=0$$

Subtract 8 from 9 to get 1.

$$3x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12}}{2\times 3}$$

Take the square root of -12.

$$x=\frac{0±2\sqrt{3}i}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{3}i}{6}$$

Now solve the equation x=\frac{0±2\sqrt{3}i}{6} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{3}i}{6} when ± is minus.

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

The equation is now solved.

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