Solve x^2-1=6

$$x ^ { 2 } - 1 = 6$$

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Add 1 to both sides.

$$x^{2}=6+1$$

Add 6 and 1 to get 7.

$$x^{2}=7$$

Take the square root of both sides of the equation.

$$x=\sqrt{7} x=-\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract 6 from both sides.

$$x^{2}-1-6=0$$

Subtract 6 from -1 to get -7.

$$x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7\right)}}{2}$$

Multiply -4 times -7.

$$x=\frac{0±\sqrt{28}}{2}$$

Take the square root of 28.

$$x=\frac{0±2\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{2} when ± is plus.

$$x=\sqrt{7}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{2} when ± is minus.

$$x=-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7} x=-\sqrt{7}$$