Solve 9n^2-64 - ScanMath

Question

Factor the expression

(3 n - 8) (3 n + 8)

Evaluate

9 n^{2} - 64

Rewrite the expression in exponential form

(3 n)^{2} - 8^{2}

Solution

(3 n - 8) (3 n + 8)

Show Solution

n_{1} = - \frac{8}{3}, n_{2} = \frac{8}{3}

Alternative Form

n_{1} = - 2. \dot{6}, n_{2} = 2. \dot{6}

Evaluate

9 n^{2} - 64

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

9 n^{2} - 64 = 0

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

9 n^{2} = 0 + 64

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

9 n^{2} = 64

Divide both sides

\frac{9 n ^{2}}{9} = \frac{64}{9}

Divide the numbers

n^{2} = \frac{64}{9}

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

n = \pm \frac{64}{9}

Simplify the expression

More Steps

Evaluate

\frac{64}{9}

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

\frac{64}{9}

Simplify the radical expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 8

8^{2}

Reduce the index of the radical and exponent with 2

8

\frac{8}{9}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{8}{3}

n = \pm \frac{8}{3}

Separate the equation into 2 possible cases

n = \frac{8}{3} n = - \frac{8}{3}

Solution

n_{1} = - \frac{8}{3}, n_{2} = \frac{8}{3}

Alternative Form

n_{1} = - 2. \dot{6}, n_{2} = 2. \dot{6}

Show Solution