Solve -4(2x 1) 4x^3=-17

Question

Solve the equation

x_{1} = - \frac{4 136}{4}, x_{2} = \frac{4 136}{4}

Alternative Form

x_{1} \approx - 0.853738, x_{2} \approx 0.853738

Evaluate

- 4 (2 x \times 1) \times 4 x^{3} = - 17

Remove the parentheses

- 4 \times 2 x \times 1 \times 4 x^{3} = - 17

Multiply the terms

More Steps

Evaluate

- 4 \times 2 x \times 1 \times 4 x^{3}

Rewrite the expression

- 4 \times 2 x \times 4 x^{3}

Multiply the terms

More Steps

Evaluate

4 \times 2 \times 4

Multiply the terms

8 \times 4

Multiply the numbers

32

- 32 x \times x^{3}

Multiply the terms with the same base by adding their exponents

- 32 x^{1 + 3}

Add the numbers

- 32 x^{4}

- 32 x^{4} = - 17

Change the signs on both sides of the equation

32 x^{4} = 17

Divide both sides

\frac{32 x ^{4}}{32} = \frac{17}{32}

Divide the numbers

x^{4} = \frac{17}{32}

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

x = \pm 4 \frac{17}{32}

Simplify the expression

More Steps

Evaluate

4 \frac{17}{32}

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

\frac{4 17}{4 32}

Simplify the radical expression

More Steps

Evaluate

432

Write the expression as a product where the root of one of the factors can be evaluated

4 16 \times 2

Write the number in exponential form with the base of 2

4 2^{4} \times 2

The root of a product is equal to the product of the roots of each factor

4 2^{4} \times 42

Reduce the index of the radical and exponent with 4

242

\frac{4 17}{2 4 2}

Multiply by the Conjugate

\frac{4 17 \times 4 2 ^{3}}{2 4 2 \times 4 2 ^{3}}

Simplify

\frac{4 17 \times 4 8}{2 4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

417 \times 48

The product of roots with the same index is equal to the root of the product

4 17 \times 8

Calculate the product

4136

\frac{4 136}{2 4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

242 \times 4 2^{3}

Multiply the terms

2 \times 2

Multiply the numbers

4

\frac{4 136}{4}

x = \pm \frac{4 136}{4}

Separate the equation into 2 possible cases

x = \frac{4 136}{4} x = - \frac{4 136}{4}

Solution

x_{1} = - \frac{4 136}{4}, x_{2} = \frac{4 136}{4}

Alternative Form

x_{1} \approx - 0.853738, x_{2} \approx 0.853738

Show Solution