Solve 121m^2 - 36

Question

Factor the expression

(11 m - 6) (11 m + 6)

Evaluate

121 m^{2} - 36

Rewrite the expression in exponential form

(11 m)^{2} - 6^{2}

Solution

(11 m - 6) (11 m + 6)

Show Solution

m_{1} = - \frac{6}{11}, m_{2} = \frac{6}{11}

Alternative Form

m_{1} = - 0. \dot{5} \dot{4}, m_{2} = 0. \dot{5} \dot{4}

Evaluate

121 m^{2} - 36

To find the roots of the expression,set the expression equal to 0

121 m^{2} - 36 = 0

Move the constant to the right-hand side and change its sign

121 m^{2} = 0 + 36

Removing 0 doesn't change the value,so remove it from the expression

121 m^{2} = 36

Divide both sides

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

Divide the numbers

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

Take the root of both sides of the equation and remember to use both positive and negative roots

m = \pm \frac{36}{121}

Simplify the expression

More Steps

Evaluate

\frac{36}{121}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{36}{121}

Simplify the radical expression

More Steps

Evaluate

36

Write the number in exponential form with the base of 6

6^{2}

Reduce the index of the radical and exponent with 2

6

\frac{6}{121}

Simplify the radical expression

More Steps

Evaluate

121

Write the number in exponential form with the base of 11

1 1^{2}

Reduce the index of the radical and exponent with 2

11

\frac{6}{11}

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

Separate the equation into 2 possible cases

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

Solution

m_{1} = - \frac{6}{11}, m_{2} = \frac{6}{11}

Alternative Form

m_{1} = - 0. \dot{5} \dot{4}, m_{2} = 0. \dot{5} \dot{4}

Show Solution