Solve M^2-81=0

$$M ^ { 2 } - 81 = 0$$

Solve for M

$$M=9$$

$$M=-9$$

Steps Using Difference of Squares

Consider M^{2}-81. Rewrite M^{2}-81 as M^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(M-9\right)\left(M+9\right)=0$$

To find equation solutions, solve M-9=0 and M+9=0.

$$M=9 M=-9$$

Steps by Finding Square Root

Add 81 to both sides. Anything plus zero gives itself.

$$M^{2}=81$$

Take the square root of both sides of the equation.

$$M=9 M=-9$$

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.

$$M^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$M=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$M=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$M=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$M=\frac{0±18}{2}$$

Now solve the equation M=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$M=9$$

Now solve the equation M=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$M=-9$$

The equation is now solved.

$$M=9 M=-9$$