Solve 3(x^5)-x = 2(x 9)

Question

Solve the equation

x_{1} = - \frac{4 513}{3}, x_{2} = 0, x_{3} = \frac{4 513}{3}

Alternative Form

x_{1} \approx - 1.586383, x_{2} = 0, x_{3} \approx 1.586383

Evaluate

3 x^{5} - x = 2 (x \times 9)

Remove the parentheses

3 x^{5} - x = 2 x \times 9

Multiply the terms

3 x^{5} - x = 18 x

Move the expression to the left side

3 x^{5} - x - 18 x = 0

Subtract the terms

More Steps

Evaluate

- x - 18 x

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

(- 1 - 18) x

Subtract the numbers

- 19 x

3 x^{5} - 19 x = 0

Factor the expression

x (3 x^{4} - 19) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{4} - 19 = 0

Solve the equation

More Steps

Evaluate

3 x^{4} - 19 = 0

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

3 x^{4} = 0 + 19

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

3 x^{4} = 19

Divide both sides

\frac{3 x ^{4}}{3} = \frac{19}{3}

Divide the numbers

x^{4} = \frac{19}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{19}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{19}{3}

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

\frac{4 19}{4 3}

Multiply by the Conjugate

\frac{4 19 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 19 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 513}{4 3 \times 4 3 ^{3}}

Multiply the numbers

\frac{4 513}{3}

x = \pm \frac{4 513}{3}

Separate the equation into 2 possible cases

x = \frac{4 513}{3} x = - \frac{4 513}{3}

x = 0 x = \frac{4 513}{3} x = - \frac{4 513}{3}

Solution

x_{1} = - \frac{4 513}{3}, x_{2} = 0, x_{3} = \frac{4 513}{3}

Alternative Form

x_{1} \approx - 1.586383, x_{2} = 0, x_{3} \approx 1.586383

Show Solution