Solve 21x-x^54x^3

Question

Simplify the expression

21 x - 4 x^{8}

Evaluate

21 x - x^{5} \times 4 x^{3}

Solution

More Steps

Evaluate

x^{5} \times 4 x^{3}

Multiply the terms with the same base by adding their exponents

x^{5 + 3} \times 4

Add the numbers

x^{8} \times 4

Use the commutative property to reorder the terms

4 x^{8}

21 x - 4 x^{8}

Show Solution

Factor the expression

x (21 - 4 x^{7})

Evaluate

21 x - x^{5} \times 4 x^{3}

Multiply

More Steps

Evaluate

x^{5} \times 4 x^{3}

Multiply the terms with the same base by adding their exponents

x^{5 + 3} \times 4

Add the numbers

x^{8} \times 4

Use the commutative property to reorder the terms

4 x^{8}

21 x - 4 x^{8}

Rewrite the expression

x \times 21 - x \times 4 x^{7}

Solution

x (21 - 4 x^{7})

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{7 672}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.267301

Evaluate

21 x - x^{5} \times 4 x^{3}

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

21 x - x^{5} \times 4 x^{3} = 0

Multiply

More Steps

Multiply the terms

x^{5} \times 4 x^{3}

Multiply the terms with the same base by adding their exponents

x^{5 + 3} \times 4

Add the numbers

x^{8} \times 4

Use the commutative property to reorder the terms

4 x^{8}

21 x - 4 x^{8} = 0

Factor the expression

x (21 - 4 x^{7}) = 0

Separate the equation into 2 possible cases

x = 0 21 - 4 x^{7} = 0

Solve the equation

More Steps

Evaluate

21 - 4 x^{7} = 0

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

- 4 x^{7} = 0 - 21

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

- 4 x^{7} = - 21

Change the signs on both sides of the equation

4 x^{7} = 21

Divide both sides

\frac{4 x ^{7}}{4} = \frac{21}{4}

Divide the numbers

x^{7} = \frac{21}{4}

Take the 7 -th root on both sides of the equation

7 x^{7} = 7 \frac{21}{4}

Calculate

x = 7 \frac{21}{4}

Simplify the root

More Steps

Evaluate

7 \frac{21}{4}

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

\frac{7 21}{7 4}

Multiply by the Conjugate

\frac{7 21 \times 7 4 ^{6}}{7 4 \times 7 4 ^{6}}

Simplify

\frac{7 21 \times 2 7 32}{7 4 \times 7 4 ^{6}}

Multiply the numbers

\frac{2 7 672}{7 4 \times 7 4 ^{6}}

Multiply the numbers

\frac{2 7 672}{2 ^{2}}

Reduce the fraction

\frac{7 672}{2}

x = \frac{7 672}{2}

x = 0 x = \frac{7 672}{2}

Solution

x_{1} = 0, x_{2} = \frac{7 672}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.267301

Show Solution