Solve 3-7b^4b=6 - ScanMath

Question

Solve the equation

b = - \frac{5 7203}{7}

Alternative Form

b \approx - 0.844121

Evaluate

3 - 7 b^{4} \times b = 6

Multiply

More Steps

Evaluate

7 b^{4} \times b

Multiply the terms with the same base by adding their exponents

7 b^{4 + 1}

Add the numbers

7 b^{5}

3 - 7 b^{5} = 6

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

- 7 b^{5} = 6 - 3

Subtract the numbers

- 7 b^{5} = 3

Change the signs on both sides of the equation

7 b^{5} = - 3

Divide both sides

\frac{7 b ^{5}}{7} = \frac{- 3}{7}

Divide the numbers

b^{5} = \frac{- 3}{7}

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

b^{5} = - \frac{3}{7}

Take the 5 -th root on both sides of the equation

5 b^{5} = 5 - \frac{3}{7}

Calculate

b = 5 - \frac{3}{7}

Solution

More Steps

Evaluate

5 - \frac{3}{7}

An odd root of a negative radicand is always a negative

- 5 \frac{3}{7}

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

- \frac{5 3}{5 7}

Multiply by the Conjugate

\frac{- 5 3 \times 5 7 ^{4}}{5 7 \times 5 7 ^{4}}

Simplify

\frac{- 5 3 \times 5 2401}{5 7 \times 5 7 ^{4}}

Multiply the numbers

More Steps

Evaluate

- 53 \times 52401

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

- 5 3 \times 2401

Calculate the product

- 57203

\frac{- 5 7203}{5 7 \times 5 7 ^{4}}

Multiply the numbers

More Steps

Evaluate

57 \times 5 7^{4}

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

5 7 \times 7^{4}

Calculate the product

5 7^{5}

Reduce the index of the radical and exponent with 5

7

\frac{- 5 7203}{7}

Calculate

- \frac{5 7203}{7}

b = - \frac{5 7203}{7}

Alternative Form

b \approx - 0.844121

Show Solution