Solve 36k^2-256 - ScanMath

Question

Factor the expression

4 (3 k - 8) (3 k + 8)

Evaluate

36 k^{2} - 256

Factor out 4 from the expression

4 (9 k^{2} - 64)

Solution

More Steps

Evaluate

9 k^{2} - 64

Rewrite the expression in exponential form

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

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(3 k - 8) (3 k + 8)

4 (3 k - 8) (3 k + 8)

Show Solution

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

Alternative Form

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

Evaluate

36 k^{2} - 256

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

36 k^{2} - 256 = 0

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

36 k^{2} = 0 + 256

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

36 k^{2} = 256

Divide both sides

\frac{36 k ^{2}}{36} = \frac{256}{36}

Divide the numbers

k^{2} = \frac{256}{36}

Cancel out the common factor 4

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

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

k = \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}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution