Solve 16x^2-81 - ScanMath

Question

Factor the expression

(4 x - 9) (4 x + 9)

Evaluate

16 x^{2} - 81

Rewrite the expression in exponential form

(4 x)^{2} - 9^{2}

Solution

(4 x - 9) (4 x + 9)

Show Solution

x_{1} = - \frac{9}{4}, x_{2} = \frac{9}{4}

Alternative Form

x_{1} = - 2.25, x_{2} = 2.25

Evaluate

16 x^{2} - 81

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

16 x^{2} - 81 = 0

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

16 x^{2} = 0 + 81

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

16 x^{2} = 81

Divide both sides

\frac{16 x ^{2}}{16} = \frac{81}{16}

Divide the numbers

x^{2} = \frac{81}{16}

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

x = \pm \frac{81}{16}

Simplify the expression

More Steps

Evaluate

\frac{81}{16}

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

\frac{81}{16}

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{9}{16}

Simplify the radical expression

More Steps

Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

\frac{9}{4}

x = \pm \frac{9}{4}

Separate the equation into 2 possible cases

x = \frac{9}{4} x = - \frac{9}{4}

Solution

x_{1} = - \frac{9}{4}, x_{2} = \frac{9}{4}

Alternative Form

x_{1} = - 2.25, x_{2} = 2.25

Show Solution