Solve -8-2 -6 -7j^3 -6

Question

Simplify the expression

- 22 - 7 j^{3}

Evaluate

- 8 - 2 - 6 - 7 j^{3} - 6

Solution

- 22 - 7 j^{3}

Show Solution

j = - \frac{3 1078}{7}

Alternative Form

j \approx - 1.464788

Evaluate

- 8 - 2 - 6 - 7 j^{3} - 6

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

- 8 - 2 - 6 - 7 j^{3} - 6 = 0

Subtract the numbers

- 10 - 6 - 7 j^{3} - 6 = 0

Subtract the numbers

- 16 - 7 j^{3} - 6 = 0

Subtract the numbers

- 22 - 7 j^{3} = 0

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

- 7 j^{3} = 0 + 22

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

- 7 j^{3} = 22

Change the signs on both sides of the equation

7 j^{3} = - 22

Divide both sides

\frac{7 j ^{3}}{7} = \frac{- 22}{7}

Divide the numbers

j^{3} = \frac{- 22}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

j^{3} = - \frac{22}{7}

Take the 3 -th root on both sides of the equation

3 j^{3} = 3 - \frac{22}{7}

Calculate

j = 3 - \frac{22}{7}

Solution

More Steps

Evaluate

3 - \frac{22}{7}

An odd root of a negative radicand is always a negative

- 3 \frac{22}{7}

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

- \frac{3 22}{3 7}

Multiply by the Conjugate

\frac{- 3 22 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{- 3 22 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 322 \times 349

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

- 3 22 \times 49

Calculate the product

- 31078

\frac{- 3 1078}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{- 3 1078}{7}

Calculate

- \frac{3 1078}{7}

j = - \frac{3 1078}{7}

Alternative Form

j \approx - 1.464788

Show Solution