Solve 4(2x 1)=5x^3x^4

Question

Solve the equation

x_{1} = - \frac{6 25000}{5}, x_{2} = 0, x_{3} = \frac{6 25000}{5}

Alternative Form

x_{1} \approx - 1.081484, x_{2} = 0, x_{3} \approx 1.081484

Evaluate

4 (2 x \times 1) = 5 x^{3} \times x^{4}

Remove the parentheses

4 \times 2 x \times 1 = 5 x^{3} \times x^{4}

Multiply the terms

More Steps

Evaluate

4 \times 2 x \times 1

Rewrite the expression

4 \times 2 x

Multiply the terms

8 x

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

5 x^{3 + 4}

Add the numbers

5 x^{7}

8 x = 5 x^{7}

Add or subtract both sides

8 x - 5 x^{7} = 0

Factor the expression

x (8 - 5 x^{6}) = 0

Separate the equation into 2 possible cases

x = 0 8 - 5 x^{6} = 0

Solve the equation

More Steps

Evaluate

8 - 5 x^{6} = 0

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

- 5 x^{6} = 0 - 8

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

- 5 x^{6} = - 8

Change the signs on both sides of the equation

5 x^{6} = 8

Divide both sides

\frac{5 x ^{6}}{5} = \frac{8}{5}

Divide the numbers

x^{6} = \frac{8}{5}

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

x = \pm 6 \frac{8}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{8}{5}

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

\frac{6 8}{6 5}

Simplify the radical expression

\frac{2}{6 5}

Multiply by the Conjugate

\frac{2 \times 6 5 ^{5}}{6 5 \times 6 5 ^{5}}

Simplify

\frac{2 \times 6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

\frac{6 25000}{6 5 \times 6 5 ^{5}}

Multiply the numbers

\frac{6 25000}{5}

x = \pm \frac{6 25000}{5}

Separate the equation into 2 possible cases

x = \frac{6 25000}{5} x = - \frac{6 25000}{5}

x = 0 x = \frac{6 25000}{5} x = - \frac{6 25000}{5}

Solution

x_{1} = - \frac{6 25000}{5}, x_{2} = 0, x_{3} = \frac{6 25000}{5}

Alternative Form

x_{1} \approx - 1.081484, x_{2} = 0, x_{3} \approx 1.081484

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