Solve 3x^2+1-18-81=0

$$3 { x }^{ 2 } +1-18-81=0$$

Solve for x

$$x = \frac{7 \sqrt{6}}{3} \approx 5.715476066$$

$$x = -\frac{7 \sqrt{6}}{3} \approx -5.715476066$$

Steps by Finding Square Root

Subtract 18 from 1 to get -17.

$$3x^{2}-17-81=0$$

Subtract 81 from -17 to get -98.

$$3x^{2}-98=0$$

Add 98 to both sides. Anything plus zero gives itself.

$$3x^{2}=98$$

Divide both sides by 3.

$$x^{2}=\frac{98}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{7\sqrt{6}}{3} x=-\frac{7\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract 18 from 1 to get -17.

$$3x^{2}-17-81=0$$

Subtract 81 from -17 to get -98.

$$3x^{2}-98=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -98 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-98\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-98\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-98\right)}}{2\times 3}$$

Multiply -12 times -98.

$$x=\frac{0±\sqrt{1176}}{2\times 3}$$

Take the square root of 1176.

$$x=\frac{0±14\sqrt{6}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±14\sqrt{6}}{6}$$

Now solve the equation x=\frac{0±14\sqrt{6}}{6} when ± is plus.

$$x=\frac{7\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±14\sqrt{6}}{6} when ± is minus.

$$x=-\frac{7\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{7\sqrt{6}}{3} x=-\frac{7\sqrt{6}}{3}$$