Solve x^2-81=2

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

Solve for x

$$x=\sqrt{83}\approx 9.110433579$$

$$x=-\sqrt{83}\approx -9.110433579$$

Steps by Finding Square Root

Add 81 to both sides.

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

Add 2 and 81 to get 83.

$$x^{2}=83$$

Take the square root of both sides of the equation.

$$x=\sqrt{83} x=-\sqrt{83}$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

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

Subtract 2 from -81 to get -83.

$$x^{2}-83=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -83 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-83\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-83\right)}}{2}$$

Multiply -4 times -83.

$$x=\frac{0±\sqrt{332}}{2}$$

Take the square root of 332.

$$x=\frac{0±2\sqrt{83}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{83}}{2} when ± is plus.

$$x=\sqrt{83}$$

Now solve the equation x=\frac{0±2\sqrt{83}}{2} when ± is minus.

$$x=-\sqrt{83}$$

The equation is now solved.

$$x=\sqrt{83} x=-\sqrt{83}$$