Solve (m^2-1)=8

$$( m ^ { 2 } - 1 ) = 8$$

Solve for m

$$m=3$$

$$m=-3$$

Steps Using Difference of Squares

Subtract 8 from both sides.

$$m^{2}-1-8=0$$

Subtract 8 from -1 to get -9.

$$m^{2}-9=0$$

Consider m^{2}-9. Rewrite m^{2}-9 as m^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m-3\right)\left(m+3\right)=0$$

To find equation solutions, solve m-3=0 and m+3=0.

$$m=3 m=-3$$

Steps by Finding Square Root

Add 1 to both sides.

$$m^{2}=8+1$$

Add 8 and 1 to get 9.

$$m^{2}=9$$

Take the square root of both sides of the equation.

$$m=3 m=-3$$

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$m^{2}-1-8=0$$

Subtract 8 from -1 to get -9.

$$m^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-9\right)}}{2}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-9\right)}}{2}$$

Multiply -4 times -9.

$$m=\frac{0±\sqrt{36}}{2}$$

Take the square root of 36.

$$m=\frac{0±6}{2}$$

Now solve the equation m=\frac{0±6}{2} when ± is plus. Divide 6 by 2.

$$m=3$$

Now solve the equation m=\frac{0±6}{2} when ± is minus. Divide -6 by 2.

$$m=-3$$

The equation is now solved.

$$m=3 m=-3$$