Solve x^2-64=18

$${ x }^{ 2 } -64=18$$

Solve for x

$$x=\sqrt{82}\approx 9.055385138$$

$$x=-\sqrt{82}\approx -9.055385138$$

Steps by Finding Square Root

Add 64 to both sides.

$$x^{2}=18+64$$

Add 18 and 64 to get 82.

$$x^{2}=82$$

Take the square root of both sides of the equation.

$$x=\sqrt{82} x=-\sqrt{82}$$

Steps Using the Quadratic Formula

Subtract 18 from both sides.

$$x^{2}-64-18=0$$

Subtract 18 from -64 to get -82.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -82 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -82.

$$x=\frac{0±\sqrt{328}}{2}$$

Take the square root of 328.

$$x=\frac{0±2\sqrt{82}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{82}}{2} when ± is plus.

$$x=\sqrt{82}$$

Now solve the equation x=\frac{0±2\sqrt{82}}{2} when ± is minus.

$$x=-\sqrt{82}$$

The equation is now solved.

$$x=\sqrt{82} x=-\sqrt{82}$$