Solve 27z^2-192 - ScanMath

Question

Factor the expression

3 (3 z - 8) (3 z + 8)

Evaluate

27 z^{2} - 192

Factor out 3 from the expression

3 (9 z^{2} - 64)

Solution

More Steps

Evaluate

9 z^{2} - 64

Rewrite the expression in exponential form

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

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

(3 z - 8) (3 z + 8)

3 (3 z - 8) (3 z + 8)

Show Solution

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

Alternative Form

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

Evaluate

27 z^{2} - 192

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

27 z^{2} - 192 = 0

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

27 z^{2} = 0 + 192

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

27 z^{2} = 192

Divide both sides

\frac{27 z ^{2}}{27} = \frac{192}{27}

Divide the numbers

z^{2} = \frac{192}{27}

Cancel out the common factor 3

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

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

z = \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}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution