Solve 3x^2+1=9

$$3 x ^ { 2 } + 1 = 9$$

Solve for x

$$x = \frac{2 \sqrt{6}}{3} \approx 1.632993162$$

$$x = -\frac{2 \sqrt{6}}{3} \approx -1.632993162$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$3x^{2}=9-1$$

Subtract 1 from 9 to get 8.

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

Divide both sides by 3.

$$x^{2}=\frac{8}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{6}}{3} x=-\frac{2\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract 9 from both sides.

$$3x^{2}+1-9=0$$

Subtract 9 from 1 to get -8.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-8\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-8\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-8\right)}}{2\times 3}$$

Multiply -12 times -8.

$$x=\frac{0±\sqrt{96}}{2\times 3}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±4\sqrt{6}}{6}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{6} when ± is plus.

$$x=\frac{2\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{6} when ± is minus.

$$x=-\frac{2\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{6}}{3} x=-\frac{2\sqrt{6}}{3}$$