Solve 6x-7/3x^4 -5x-7/3x^4

Question

Simplify the expression

Solution

x - \frac{14}{3} x^{4}

Evaluate

6 x - \frac{7}{3} x^{4} - 5 x - \frac{7}{3} x^{4}

Subtract the terms

More Steps

Evaluate

6 x - 5 x

Collect like terms by calculating the sum or difference of their coefficients

(6 - 5) x

Subtract the numbers

x

x - \frac{7}{3} x^{4} - \frac{7}{3} x^{4}

Solution

More Steps

Evaluate

- \frac{7}{3} x^{4} - \frac{7}{3} x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(- \frac{7}{3} - \frac{7}{3}) x^{4}

Subtract the numbers

More Steps

Evaluate

- \frac{7}{3} - \frac{7}{3}

Write all numerators above the common denominator

\frac{- 7 - 7}{3}

Subtract the numbers

\frac{- 14}{3}

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

- \frac{14}{3}

- \frac{14}{3} x^{4}

x - \frac{14}{3} x^{4}

Show Solution

Factor the expression

Factor

\frac{1}{3} x (3 - 14 x^{3})

Evaluate

6 x - \frac{7}{3} x^{4} - 5 x - \frac{7}{3} x^{4}

Subtract the terms

More Steps

Simplify

6 x - \frac{7}{3} x^{4} - 5 x

Subtract the terms

More Steps

Evaluate

6 x - 5 x

Collect like terms by calculating the sum or difference of their coefficients

(6 - 5) x

Subtract the numbers

x

x - \frac{7}{3} x^{4}

x - \frac{7}{3} x^{4} - \frac{7}{3} x^{4}

Subtract the terms

More Steps

Evaluate

- \frac{7}{3} x^{4} - \frac{7}{3} x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(- \frac{7}{3} - \frac{7}{3}) x^{4}

Subtract the numbers

More Steps

Evaluate

- \frac{7}{3} - \frac{7}{3}

Write all numerators above the common denominator

\frac{- 7 - 7}{3}

Subtract the numbers

\frac{- 14}{3}

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

- \frac{14}{3}

- \frac{14}{3} x^{4}

x - \frac{14}{3} x^{4}

Rewrite the expression

\frac{1}{3} x \times 3 - \frac{1}{3} x \times 14 x^{3}

Solution

\frac{1}{3} x (3 - 14 x^{3})

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = 0, x_{2} = \frac{3 588}{14}

Alternative Form

x_{1} = 0, x_{2} \approx 0.598408

Evaluate

6 x - \frac{7}{3} x^{4} - 5 x - \frac{7}{3} x^{4}

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

6 x - \frac{7}{3} x^{4} - 5 x - \frac{7}{3} x^{4} = 0

Subtract the terms

More Steps

Simplify

6 x - \frac{7}{3} x^{4} - 5 x

Subtract the terms

More Steps

Evaluate

6 x - 5 x

Collect like terms by calculating the sum or difference of their coefficients

(6 - 5) x

Subtract the numbers

x

x - \frac{7}{3} x^{4}

x - \frac{7}{3} x^{4} - \frac{7}{3} x^{4} = 0

Subtract the terms

More Steps

Simplify

x - \frac{7}{3} x^{4} - \frac{7}{3} x^{4}

Subtract the terms

More Steps

Evaluate

- \frac{7}{3} x^{4} - \frac{7}{3} x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(- \frac{7}{3} - \frac{7}{3}) x^{4}

Subtract the numbers

- \frac{14}{3} x^{4}

x - \frac{14}{3} x^{4}

x - \frac{14}{3} x^{4} = 0

Factor the expression

x (1 - \frac{14}{3} x^{3}) = 0

Separate the equation into 2 possible cases

x = 0 1 - \frac{14}{3} x^{3} = 0

Solve the equation

More Steps

Evaluate

1 - \frac{14}{3} x^{3} = 0

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

- \frac{14}{3} x^{3} = 0 - 1

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

- \frac{14}{3} x^{3} = - 1

Change the signs on both sides of the equation

\frac{14}{3} x^{3} = 1

Multiply by the reciprocal

\frac{14}{3} x^{3} \times \frac{3}{14} = 1 \times \frac{3}{14}

Multiply

x^{3} = 1 \times \frac{3}{14}

Any expression multiplied by 1 remains the same

x^{3} = \frac{3}{14}

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

3 x^{3} = 3 \frac{3}{14}

Calculate

x = 3 \frac{3}{14}

Simplify the root

More Steps

Evaluate

3 \frac{3}{14}

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

\frac{3 3}{3 14}

Multiply by the Conjugate

\frac{3 3 \times 3 1 4 ^{2}}{3 14 \times 3 1 4 ^{2}}

Simplify

\frac{3 3 \times 3 196}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

\frac{3 588}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

\frac{3 588}{14}

x = \frac{3 588}{14}

x = 0 x = \frac{3 588}{14}

Solution

x_{1} = 0, x_{2} = \frac{3 588}{14}

Alternative Form

x_{1} = 0, x_{2} \approx 0.598408

Show Solution

6x 7/3x^4 5x 7/3x^4

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression