Solve (x^2-1)=13

$$( x ^ { 2 } - 1 ) = 13$$

Solve for x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Add 1 to both sides.

$$x^{2}=13+1$$

Add 13 and 1 to get 14.

$$x^{2}=14$$

Take the square root of both sides of the equation.

$$x=\sqrt{14} x=-\sqrt{14}$$

Steps Using the Quadratic Formula

Subtract 13 from both sides.

$$x^{2}-1-13=0$$

Subtract 13 from -1 to get -14.

$$x^{2}-14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-14\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-14\right)}}{2}$$

Multiply -4 times -14.

$$x=\frac{0±\sqrt{56}}{2}$$

Take the square root of 56.

$$x=\frac{0±2\sqrt{14}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{14}}{2} when ± is plus.

$$x=\sqrt{14}$$

Now solve the equation x=\frac{0±2\sqrt{14}}{2} when ± is minus.

$$x=-\sqrt{14}$$

The equation is now solved.

$$x=\sqrt{14} x=-\sqrt{14}$$