Solve x^2-1=21

$${ x }^{ 2 } -1=21$$

Solve for x

$$x=\sqrt{22}\approx 4.69041576$$

$$x=-\sqrt{22}\approx -4.69041576$$

Steps by Finding Square Root

Add 1 to both sides.

$$x^{2}=21+1$$

Add 21 and 1 to get 22.

$$x^{2}=22$$

Take the square root of both sides of the equation.

$$x=\sqrt{22} x=-\sqrt{22}$$

Steps Using the Quadratic Formula

Subtract 21 from both sides.

$$x^{2}-1-21=0$$

Subtract 21 from -1 to get -22.

$$x^{2}-22=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -22 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-22\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-22\right)}}{2}$$

Multiply -4 times -22.

$$x=\frac{0±\sqrt{88}}{2}$$

Take the square root of 88.

$$x=\frac{0±2\sqrt{22}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{22}}{2} when ± is plus.

$$x=\sqrt{22}$$

Now solve the equation x=\frac{0±2\sqrt{22}}{2} when ± is minus.

$$x=-\sqrt{22}$$

The equation is now solved.

$$x=\sqrt{22} x=-\sqrt{22}$$