Solve 121x^2-25 - ScanMath

Question

Factor the expression

(11 x - 5) (11 x + 5)

Evaluate

121 x^{2} - 25

Rewrite the expression in exponential form

(11 x)^{2} - 5^{2}

Solution

(11 x - 5) (11 x + 5)

Show Solution

x_{1} = - \frac{5}{11}, x_{2} = \frac{5}{11}

Alternative Form

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

Evaluate

121 x^{2} - 25

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

121 x^{2} - 25 = 0

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

121 x^{2} = 0 + 25

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

121 x^{2} = 25

Divide both sides

\frac{121 x ^{2}}{121} = \frac{25}{121}

Divide the numbers

x^{2} = \frac{25}{121}

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

x = \pm \frac{25}{121}

Simplify the expression

More Steps

Evaluate

\frac{25}{121}

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

\frac{25}{121}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{5}{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{5}{11}

x = \pm \frac{5}{11}

Separate the equation into 2 possible cases

x = \frac{5}{11} x = - \frac{5}{11}

Solution

x_{1} = - \frac{5}{11}, x_{2} = \frac{5}{11}

Alternative Form

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

Show Solution