Solve 9m^2-9=0

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

Solve for m

$$m=1$$

$$m=-1$$

Steps Using Difference of Squares

Divide both sides by 9.

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

Consider m^{2}-1. Rewrite m^{2}-1 as m^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(m-1\right)\left(m+1\right)=0$$

To find equation solutions, solve m-1=0 and m+1=0.

$$m=1 m=-1$$

Steps by Finding Square Root

Add 9 to both sides. Anything plus zero gives itself.

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

Divide both sides by 9.

$$m^{2}=\frac{9}{9}$$

Divide 9 by 9 to get 1.

$$m^{2}=1$$

Take the square root of both sides of the equation.

$$m=1 m=-1$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

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

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

Square 0.

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

Multiply -4 times 9.

$$m=\frac{0±\sqrt{-36\left(-9\right)}}{2\times 9}$$

Multiply -36 times -9.

$$m=\frac{0±\sqrt{324}}{2\times 9}$$

Take the square root of 324.

$$m=\frac{0±18}{2\times 9}$$

Multiply 2 times 9.

$$m=\frac{0±18}{18}$$

Now solve the equation m=\frac{0±18}{18} when ± is plus. Divide 18 by 18.

$$m=1$$

Now solve the equation m=\frac{0±18}{18} when ± is minus. Divide -18 by 18.

$$m=-1$$

The equation is now solved.

$$m=1 m=-1$$