Solve 7z^38=10z 8

Question

Solve the equation

z_{1} = - \frac{70}{7}, z_{2} = 0, z_{3} = \frac{70}{7}

Alternative Form

z_{1} \approx - 1.195229, z_{2} = 0, z_{3} \approx 1.195229

Evaluate

7 z^{3} \times 8 = 10 z \times 8

Simplify

7 z^{3} = 10 z

Add or subtract both sides

7 z^{3} - 10 z = 0

Factor the expression

z (7 z^{2} - 10) = 0

Separate the equation into 2 possible cases

z = 0 7 z^{2} - 10 = 0

Solve the equation

More Steps

Evaluate

7 z^{2} - 10 = 0

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

7 z^{2} = 0 + 10

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

7 z^{2} = 10

Divide both sides

\frac{7 z ^{2}}{7} = \frac{10}{7}

Divide the numbers

z^{2} = \frac{10}{7}

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

z = \pm \frac{10}{7}

Simplify the expression

More Steps

Evaluate

\frac{10}{7}

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

\frac{10}{7}

Multiply by the Conjugate

\frac{10 \times 7}{7 \times 7}

Multiply the numbers

\frac{70}{7 \times 7}

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

\frac{70}{7}

z = \pm \frac{70}{7}

Separate the equation into 2 possible cases

z = \frac{70}{7} z = - \frac{70}{7}

z = 0 z = \frac{70}{7} z = - \frac{70}{7}

Solution

z_{1} = - \frac{70}{7}, z_{2} = 0, z_{3} = \frac{70}{7}

Alternative Form

z_{1} \approx - 1.195229, z_{2} = 0, z_{3} \approx 1.195229

Show Solution