Solve -12 = -2z^37z

Question

Solve the equation

z_{1} = - \frac{4 2058}{7}, z_{2} = \frac{4 2058}{7}

Alternative Form

z_{1} \approx - 0.962195, z_{2} \approx 0.962195

Evaluate

- 12 = - 2 z^{3} \times 7 z

Multiply

More Steps

Evaluate

- 2 z^{3} \times 7 z

Multiply the terms

- 14 z^{3} \times z

Multiply the terms with the same base by adding their exponents

- 14 z^{3 + 1}

Add the numbers

- 14 z^{4}

- 12 = - 14 z^{4}

Swap the sides of the equation

- 14 z^{4} = - 12

Change the signs on both sides of the equation

14 z^{4} = 12

Divide both sides

\frac{14 z ^{4}}{14} = \frac{12}{14}

Divide the numbers

z^{4} = \frac{12}{14}

Cancel out the common factor 2

z^{4} = \frac{6}{7}

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

z = \pm 4 \frac{6}{7}

Simplify the expression

More Steps

Evaluate

4 \frac{6}{7}

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

\frac{4 6}{4 7}

Multiply by the Conjugate

\frac{4 6 \times 4 7 ^{3}}{4 7 \times 4 7 ^{3}}

Simplify

\frac{4 6 \times 4 343}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

46 \times 4343

The product of roots with the same index is equal to the root of the product

4 6 \times 343

Calculate the product

42058

\frac{4 2058}{4 7 \times 4 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

47 \times 4 7^{3}

The product of roots with the same index is equal to the root of the product

4 7 \times 7^{3}

Calculate the product

4 7^{4}

Reduce the index of the radical and exponent with 4

7

\frac{4 2058}{7}

z = \pm \frac{4 2058}{7}

Separate the equation into 2 possible cases

z = \frac{4 2058}{7} z = - \frac{4 2058}{7}

Solution

z_{1} = - \frac{4 2058}{7}, z_{2} = \frac{4 2058}{7}

Alternative Form

z_{1} \approx - 0.962195, z_{2} \approx 0.962195

Show Solution