Solve 121m^2-99=-63

$$121 m ^ { 2 } - 99 = - 63$$

Solve for m

$$m=\frac{6}{11}\approx 0.545454545$$

$$m=-\frac{6}{11}\approx -0.545454545$$

Steps Using Difference of Squares

Add 63 to both sides.

$$121m^{2}-99+63=0$$

Add -99 and 63 to get -36.

$$121m^{2}-36=0$$

Consider 121m^{2}-36. Rewrite 121m^{2}-36 as \left(11m\right)^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(11m-6\right)\left(11m+6\right)=0$$

To find equation solutions, solve 11m-6=0 and 11m+6=0.

$$m=\frac{6}{11} m=-\frac{6}{11}$$

Steps by Finding Square Root

Add 99 to both sides.

$$121m^{2}=-63+99$$

Add -63 and 99 to get 36.

$$121m^{2}=36$$

Divide both sides by 121.

$$m^{2}=\frac{36}{121}$$

Take the square root of both sides of the equation.

$$m=\frac{6}{11} m=-\frac{6}{11}$$

Steps Using the Quadratic Formula

Add 63 to both sides.

$$121m^{2}-99+63=0$$

Add -99 and 63 to get -36.

$$121m^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 121 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 121\left(-36\right)}}{2\times 121}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 121\left(-36\right)}}{2\times 121}$$

Multiply -4 times 121.

$$m=\frac{0±\sqrt{-484\left(-36\right)}}{2\times 121}$$

Multiply -484 times -36.

$$m=\frac{0±\sqrt{17424}}{2\times 121}$$

Take the square root of 17424.

$$m=\frac{0±132}{2\times 121}$$

Multiply 2 times 121.

$$m=\frac{0±132}{242}$$

Now solve the equation m=\frac{0±132}{242} when ± is plus. Reduce the fraction \frac{132}{242} to lowest terms by extracting and canceling out 22.

$$m=\frac{6}{11}$$

Now solve the equation m=\frac{0±132}{242} when ± is minus. Reduce the fraction \frac{-132}{242} to lowest terms by extracting and canceling out 22.

$$m=-\frac{6}{11}$$

The equation is now solved.

$$m=\frac{6}{11} m=-\frac{6}{11}$$