Solve x^2-100=320

$$x ^ { 2 } - 100 = 320$$

Solve for x

$$x=2\sqrt{105}\approx 20.493901532$$

$$x=-2\sqrt{105}\approx -20.493901532$$

Steps by Finding Square Root

Add 100 to both sides.

$$x^{2}=320+100$$

Add 320 and 100 to get 420.

$$x^{2}=420$$

Take the square root of both sides of the equation.

$$x=2\sqrt{105} x=-2\sqrt{105}$$

Steps Using the Quadratic Formula

Subtract 320 from both sides.

$$x^{2}-100-320=0$$

Subtract 320 from -100 to get -420.

$$x^{2}-420=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -420 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-420\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-420\right)}}{2}$$

Multiply -4 times -420.

$$x=\frac{0±\sqrt{1680}}{2}$$

Take the square root of 1680.

$$x=\frac{0±4\sqrt{105}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{105}}{2} when ± is plus.

$$x=2\sqrt{105}$$

Now solve the equation x=\frac{0±4\sqrt{105}}{2} when ± is minus.

$$x=-2\sqrt{105}$$

The equation is now solved.

$$x=2\sqrt{105} x=-2\sqrt{105}$$