Solve 8^2=x^2-1

$$8 ^ { 2 } = x ^ { 2 } - 1$$

Solve for x

$$x=\sqrt{65}\approx 8.062257748$$

$$x=-\sqrt{65}\approx -8.062257748$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$64=x^{2}-1$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-1=64$$

Add 1 to both sides.

$$x^{2}=64+1$$

Add 64 and 1 to get 65.

$$x^{2}=65$$

Take the square root of both sides of the equation.

$$x=\sqrt{65} x=-\sqrt{65}$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$64=x^{2}-1$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-1=64$$

Subtract 64 from both sides.

$$x^{2}-1-64=0$$

Subtract 64 from -1 to get -65.

$$x^{2}-65=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -65 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-65\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-65\right)}}{2}$$

Multiply -4 times -65.

$$x=\frac{0±\sqrt{260}}{2}$$

Take the square root of 260.

$$x=\frac{0±2\sqrt{65}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{65}}{2} when ± is plus.

$$x=\sqrt{65}$$

Now solve the equation x=\frac{0±2\sqrt{65}}{2} when ± is minus.

$$x=-\sqrt{65}$$

The equation is now solved.

$$x=\sqrt{65} x=-\sqrt{65}$$