Solve 8v^3 - 5v - ScanMath

Question

Factor the expression

v (8 v^{2} - 5)

Evaluate

8 v^{3} - 5 v

Rewrite the expression

v \times 8 v^{2} - v \times 5

Solution

v (8 v^{2} - 5)

Show Solution

v_{1} = - \frac{10}{4}, v_{2} = 0, v_{3} = \frac{10}{4}

Alternative Form

v_{1} \approx - 0.790569, v_{2} = 0, v_{3} \approx 0.790569

Evaluate

8 v^{3} - 5 v

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

8 v^{3} - 5 v = 0

Factor the expression

v (8 v^{2} - 5) = 0

Separate the equation into 2 possible cases

v = 0 8 v^{2} - 5 = 0

Solve the equation

More Steps

Evaluate

8 v^{2} - 5 = 0

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

8 v^{2} = 0 + 5

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

8 v^{2} = 5

Divide both sides

\frac{8 v ^{2}}{8} = \frac{5}{8}

Divide the numbers

v^{2} = \frac{5}{8}

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

v = \pm \frac{5}{8}

Simplify the expression

More Steps

Evaluate

\frac{5}{8}

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

\frac{5}{8}

Simplify the radical expression

\frac{5}{2 2}

Multiply by the Conjugate

\frac{5 \times 2}{2 2 \times 2}

Multiply the numbers

\frac{10}{2 2 \times 2}

Multiply the numbers

\frac{10}{4}

v = \pm \frac{10}{4}

Separate the equation into 2 possible cases

v = \frac{10}{4} v = - \frac{10}{4}

v = 0 v = \frac{10}{4} v = - \frac{10}{4}

Solution

v_{1} = - \frac{10}{4}, v_{2} = 0, v_{3} = \frac{10}{4}

Alternative Form

v_{1} \approx - 0.790569, v_{2} = 0, v_{3} \approx 0.790569

Show Solution