Solve 5x-x 7x 7x^3x

Question

Simplify the expression

5 x - 49 x^{6}

Evaluate

5 x - x \times 7 x \times 7 x^{3} \times x

Rewrite the expression in exponential form

5 x - x^{3} \times 7 \times 7 x^{3}

Solution

More Steps

Multiply the terms

x^{3} \times 7 \times 7 x^{3}

Multiply the terms with the same base by adding their exponents

x^{3 + 3} \times 7 \times 7

Add the numbers

x^{6} \times 7 \times 7

Multiply the terms

x^{6} \times 49

Use the commutative property to reorder the terms

49 x^{6}

5 x - 49 x^{6}

Show Solution

Factor the expression

x (5 - 49 x^{5})

Evaluate

5 x - x \times 7 x \times 7 x^{3} \times x

Multiply

More Steps

Evaluate

x \times 7 x \times 7 x^{3} \times x

Multiply the terms with the same base by adding their exponents

x^{1 + 3 + 1} \times 7 x \times 7

Add the numbers

x^{5} \times 7 x \times 7

Multiply the terms

x^{5} \times 49 x

Multiply the terms with the same base by adding their exponents

49 x^{1 + 5}

Add the numbers

49 x^{6}

5 x - 49 x^{6}

Rewrite the expression

x \times 5 - x \times 49 x^{5}

Solution

x (5 - 49 x^{5})

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5 1715}{7}

Alternative Form

x_{1} = 0, x_{2} \approx 0.633512

Evaluate

5 x - x \times 7 x \times 7 x^{3} \times x

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

5 x - x \times 7 x \times 7 x^{3} \times x = 0

Multiply

More Steps

Multiply the terms

x \times 7 x \times 7 x^{3} \times x

Multiply the terms with the same base by adding their exponents

x^{1 + 3 + 1} \times 7 x \times 7

Add the numbers

x^{5} \times 7 x \times 7

Multiply the terms

x^{5} \times 49 x

Multiply the terms with the same base by adding their exponents

49 x^{1 + 5}

Add the numbers

49 x^{6}

5 x - 49 x^{6} = 0

Factor the expression

x (5 - 49 x^{5}) = 0

Separate the equation into 2 possible cases

x = 0 5 - 49 x^{5} = 0

Solve the equation

More Steps

Evaluate

5 - 49 x^{5} = 0

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

- 49 x^{5} = 0 - 5

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

- 49 x^{5} = - 5

Change the signs on both sides of the equation

49 x^{5} = 5

Divide both sides

\frac{49 x ^{5}}{49} = \frac{5}{49}

Divide the numbers

x^{5} = \frac{5}{49}

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

5 x^{5} = 5 \frac{5}{49}

Calculate

x = 5 \frac{5}{49}

Simplify the root

More Steps

Evaluate

5 \frac{5}{49}

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

\frac{5 5}{5 49}

Multiply by the Conjugate

\frac{5 5 \times 5 4 9 ^{4}}{5 49 \times 5 4 9 ^{4}}

Simplify

\frac{5 5 \times 7 5 343}{5 49 \times 5 4 9 ^{4}}

Multiply the numbers

\frac{7 5 1715}{5 49 \times 5 4 9 ^{4}}

Multiply the numbers

\frac{7 5 1715}{7 ^{2}}

Reduce the fraction

\frac{5 1715}{7}

x = \frac{5 1715}{7}

x = 0 x = \frac{5 1715}{7}

Solution

x_{1} = 0, x_{2} = \frac{5 1715}{7}

Alternative Form

x_{1} = 0, x_{2} \approx 0.633512

Show Solution