Solve 3x^2-81=1

$$3 { x }^{ 2 } -81=1$$

Solve for x

$$x = \frac{\sqrt{246}}{3} \approx 5.228129047$$

$$x = -\frac{\sqrt{246}}{3} \approx -5.228129047$$

Steps by Finding Square Root

Add 81 to both sides.

$$3x^{2}=1+81$$

Add 1 and 81 to get 82.

$$3x^{2}=82$$

Divide both sides by 3.

$$x^{2}=\frac{82}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{246}}{3} x=-\frac{\sqrt{246}}{3}$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$3x^{2}-81-1=0$$

Subtract 1 from -81 to get -82.

$$3x^{2}-82=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -82 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-82\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-82\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-82\right)}}{2\times 3}$$

Multiply -12 times -82.

$$x=\frac{0±\sqrt{984}}{2\times 3}$$

Take the square root of 984.

$$x=\frac{0±2\sqrt{246}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{246}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{246}}{6} when ± is plus.

$$x=\frac{\sqrt{246}}{3}$$

Now solve the equation x=\frac{0±2\sqrt{246}}{6} when ± is minus.

$$x=-\frac{\sqrt{246}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{246}}{3} x=-\frac{\sqrt{246}}{3}$$