Solve 180-600 e z^6

Question

Factor the expression

60 (3 - 10 e z^{6})

Evaluate

180 - 600 e z^{6}

Solution

60 (3 - 10 e z^{6})

Show Solution

z_{1} = - \frac{6 3 \times 1 0 ^{5} e ^{5}}{10 e}, z_{2} = \frac{6 3 \times 1 0 ^{5} e ^{5}}{10 e}

Alternative Form

z_{1} \approx - 0.692582, z_{2} \approx 0.692582

Evaluate

180 - 600 e z^{6}

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

180 - 600 e z^{6} = 0

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

- 600 e z^{6} = 0 - 180

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

- 600 e z^{6} = - 180

Change the signs on both sides of the equation

600 e z^{6} = 180

Divide both sides

\frac{600 e z ^{6}}{600 e} = \frac{180}{600 e}

Divide the numbers

z^{6} = \frac{180}{600 e}

Cancel out the common factor 60

z^{6} = \frac{3}{10 e}

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

z = \pm 6 \frac{3}{10 e}

Simplify the expression

More Steps

Evaluate

6 \frac{3}{10 e}

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

\frac{6 3}{6 10 e}

Multiply by the Conjugate

\frac{6 3 \times 6 1 0 ^{5} e ^{5}}{6 10 e \times 6 1 0 ^{5} e ^{5}}

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

\frac{6 3 \times 1 0 ^{5} e ^{5}}{6 10 e \times 6 1 0 ^{5} e ^{5}}

Multiply the numbers

More Steps

Evaluate

6 10 e \times 6 1 0^{5} e^{5}

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

6 10 e \times 1 0^{5} e^{5}

Calculate the product

6 1 0^{6} e^{6}

Calculate

10 e

\frac{6 3 \times 1 0 ^{5} e ^{5}}{10 e}

z = \pm \frac{6 3 \times 1 0 ^{5} e ^{5}}{10 e}

Separate the equation into 2 possible cases

z = \frac{6 3 \times 1 0 ^{5} e ^{5}}{10 e} z = - \frac{6 3 \times 1 0 ^{5} e ^{5}}{10 e}

Solution

z_{1} = - \frac{6 3 \times 1 0 ^{5} e ^{5}}{10 e}, z_{2} = \frac{6 3 \times 1 0 ^{5} e ^{5}}{10 e}

Alternative Form

z_{1} \approx - 0.692582, z_{2} \approx 0.692582

Show Solution