Solve 81x^2 - 100

Question

Factor the expression

(9 x - 10) (9 x + 10)

Evaluate

81 x^{2} - 100

Rewrite the expression in exponential form

(9 x)^{2} - 1 0^{2}

Solution

(9 x - 10) (9 x + 10)

Show Solution

x_{1} = - \frac{10}{9}, x_{2} = \frac{10}{9}

Alternative Form

x_{1} = - 1. \dot{1}, x_{2} = 1. \dot{1}

Evaluate

81 x^{2} - 100

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

81 x^{2} - 100 = 0

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

81 x^{2} = 0 + 100

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

81 x^{2} = 100

Divide both sides

\frac{81 x ^{2}}{81} = \frac{100}{81}

Divide the numbers

x^{2} = \frac{100}{81}

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

x = \pm \frac{100}{81}

Simplify the expression

More Steps

Evaluate

\frac{100}{81}

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

\frac{100}{81}

Simplify the radical expression

More Steps

Evaluate

100

Write the number in exponential form with the base of 10

1 0^{2}

Reduce the index of the radical and exponent with 2

10

\frac{10}{81}

Simplify the radical expression

More Steps

Evaluate

81

Write the number in exponential form with the base of 9

9^{2}

Reduce the index of the radical and exponent with 2

9

\frac{10}{9}

x = \pm \frac{10}{9}

Separate the equation into 2 possible cases

x = \frac{10}{9} x = - \frac{10}{9}

Solution

x_{1} = - \frac{10}{9}, x_{2} = \frac{10}{9}

Alternative Form

x_{1} = - 1. \dot{1}, x_{2} = 1. \dot{1}

Show Solution