Solve 25x^2 - 121

Question

Factor the expression

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

Evaluate

25 x^{2} - 121

Rewrite the expression in exponential form

(5 x)^{2} - 1 1^{2}

Solution

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

Show Solution

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

Alternative Form

x_{1} = - 2.2, x_{2} = 2.2

Evaluate

25 x^{2} - 121

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

25 x^{2} - 121 = 0

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

25 x^{2} = 0 + 121

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

25 x^{2} = 121

Divide both sides

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

Divide the numbers

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{121}{25}

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

\frac{121}{25}

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{11}{25}

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{11}{5}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

x_{1} = - 2.2, x_{2} = 2.2

Show Solution