Solve [x^2-1]=7

$$[ x ^ { 2 } - 1 ] = 7$$

Solve for x

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Add 1 to both sides.

$$x^{2}=7+1$$

Add 7 and 1 to get 8.

$$x^{2}=8$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$x^{2}-1-7=0$$

Subtract 7 from -1 to get -8.

$$x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-8\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-8\right)}}{2}$$

Multiply -4 times -8.

$$x=\frac{0±\sqrt{32}}{2}$$

Take the square root of 32.

$$x=\frac{0±4\sqrt{2}}{2}$$

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

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

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

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

The equation is now solved.

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