Solve 5x-4(x^5)=3x 1

Question

Solve the equation

x_{1} = - \frac{4 8}{2}, x_{2} = 0, x_{3} = \frac{4 8}{2}

Alternative Form

x_{1} \approx - 0.840896, x_{2} = 0, x_{3} \approx 0.840896

Evaluate

5 x - 4 x^{5} = 3 x \times 1

Multiply the terms

5 x - 4 x^{5} = 3 x

Move the expression to the left side

5 x - 4 x^{5} - 3 x = 0

Subtract the terms

More Steps

Evaluate

5 x - 3 x

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

(5 - 3) x

Subtract the numbers

2 x

2 x - 4 x^{5} = 0

Factor the expression

2 x (1 - 2 x^{4}) = 0

Divide both sides

x (1 - 2 x^{4}) = 0

Separate the equation into 2 possible cases

x = 0 1 - 2 x^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 2 x^{4} = 0

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

- 2 x^{4} = 0 - 1

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

- 2 x^{4} = - 1

Change the signs on both sides of the equation

2 x^{4} = 1

Divide both sides

\frac{2 x ^{4}}{2} = \frac{1}{2}

Divide the numbers

x^{4} = \frac{1}{2}

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

x = \pm 4 \frac{1}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{2}

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

\frac{4 1}{4 2}

Simplify the radical expression

\frac{1}{4 2}

Multiply by the Conjugate

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

Simplify

\frac{4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

\frac{4 8}{2}

x = \pm \frac{4 8}{2}

Separate the equation into 2 possible cases

x = \frac{4 8}{2} x = - \frac{4 8}{2}

x = 0 x = \frac{4 8}{2} x = - \frac{4 8}{2}

Solution

x_{1} = - \frac{4 8}{2}, x_{2} = 0, x_{3} = \frac{4 8}{2}

Alternative Form

x_{1} \approx - 0.840896, x_{2} = 0, x_{3} \approx 0.840896

Show Solution