Solve 121x^2 - 49

Question

Factor the expression

(11 x - 7) (11 x + 7)

Evaluate

121 x^{2} - 49

Rewrite the expression in exponential form

(11 x)^{2} - 7^{2}

Solution

(11 x - 7) (11 x + 7)

Show Solution

x_{1} = - \frac{7}{11}, x_{2} = \frac{7}{11}

Alternative Form

x_{1} = - 0. \dot{6} \dot{3}, x_{2} = 0. \dot{6} \dot{3}

Evaluate

121 x^{2} - 49

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

121 x^{2} - 49 = 0

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

121 x^{2} = 0 + 49

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

121 x^{2} = 49

Divide both sides

\frac{121 x ^{2}}{121} = \frac{49}{121}

Divide the numbers

x^{2} = \frac{49}{121}

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

x = \pm \frac{49}{121}

Simplify the expression

More Steps

Evaluate

\frac{49}{121}

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

\frac{49}{121}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 7

7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{7}{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{7}{11}

x = \pm \frac{7}{11}

Separate the equation into 2 possible cases

x = \frac{7}{11} x = - \frac{7}{11}

Solution

x_{1} = - \frac{7}{11}, x_{2} = \frac{7}{11}

Alternative Form

x_{1} = - 0. \dot{6} \dot{3}, x_{2} = 0. \dot{6} \dot{3}

Show Solution