Solve 4z^3=62z - ScanMath

Question

Solve the equation

z_{1} = - \frac{62}{2}, z_{2} = 0, z_{3} = \frac{62}{2}

Alternative Form

z_{1} \approx - 3.937004, z_{2} = 0, z_{3} \approx 3.937004

Evaluate

4 z^{3} = 62 z

Add or subtract both sides

4 z^{3} - 62 z = 0

Factor the expression

2 z (2 z^{2} - 31) = 0

Divide both sides

z (2 z^{2} - 31) = 0

Separate the equation into 2 possible cases

z = 0 2 z^{2} - 31 = 0

Solve the equation

More Steps

Evaluate

2 z^{2} - 31 = 0

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

2 z^{2} = 0 + 31

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

2 z^{2} = 31

Divide both sides

\frac{2 z ^{2}}{2} = \frac{31}{2}

Divide the numbers

z^{2} = \frac{31}{2}

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

z = \pm \frac{31}{2}

Simplify the expression

More Steps

Evaluate

\frac{31}{2}

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

\frac{31}{2}

Multiply by the Conjugate

\frac{31 \times 2}{2 \times 2}

Multiply the numbers

\frac{62}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{62}{2}

z = \pm \frac{62}{2}

Separate the equation into 2 possible cases

z = \frac{62}{2} z = - \frac{62}{2}

z = 0 z = \frac{62}{2} z = - \frac{62}{2}

Solution

z_{1} = - \frac{62}{2}, z_{2} = 0, z_{3} = \frac{62}{2}

Alternative Form

z_{1} \approx - 3.937004, z_{2} = 0, z_{3} \approx 3.937004

Show Solution