Solve 2(2x^5) 4x-4=30

Question

Solve the equation

x_{1} = - \frac{6 136}{2}, x_{2} = \frac{6 136}{2}

Alternative Form

x_{1} \approx - 1.133861, x_{2} \approx 1.133861

Evaluate

2 \times 2 x^{5} \times 4 x - 4 = 30

Multiply

More Steps

Evaluate

2 \times 2 x^{5} \times 4 x

Multiply the terms

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Evaluate

2 \times 2 \times 4

Multiply the terms

4 \times 4

Multiply the numbers

16

16 x^{5} \times x

Multiply the terms with the same base by adding their exponents

16 x^{5 + 1}

Add the numbers

16 x^{6}

16 x^{6} - 4 = 30

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

16 x^{6} = 30 + 4

Add the numbers

16 x^{6} = 34

Divide both sides

\frac{16 x ^{6}}{16} = \frac{34}{16}

Divide the numbers

x^{6} = \frac{34}{16}

Cancel out the common factor 2

x^{6} = \frac{17}{8}

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

x = \pm 6 \frac{17}{8}

Simplify the expression

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Evaluate

6 \frac{17}{8}

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

\frac{6 17}{6 8}

Simplify the radical expression

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Evaluate

68

Write the number in exponential form with the base of 2

6 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{6 17}{2}

Multiply by the Conjugate

\frac{6 17 \times 2}{2 \times 2}

Multiply the numbers

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Evaluate

617 \times 2

Use n a = mn a^{m} to expand the expression

617 \times 6 2^{3}

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

6 17 \times 2^{3}

Calculate the product

6136

\frac{6 136}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6 136}{2}

x = \pm \frac{6 136}{2}

Separate the equation into 2 possible cases

x = \frac{6 136}{2} x = - \frac{6 136}{2}

Solution

x_{1} = - \frac{6 136}{2}, x_{2} = \frac{6 136}{2}

Alternative Form

x_{1} \approx - 1.133861, x_{2} \approx 1.133861

Show Solution