Solve 2x^35x^2 x-2

Question

Simplify the expression

10 x^{6} - 2

Evaluate

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

Solution

More Steps

Evaluate

2 x^{3} \times 5 x^{2} \times x

Multiply the terms

10 x^{3} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{3 + 2 + 1}

Add the numbers

10 x^{6}

10 x^{6} - 2

Show Solution

Factor the expression

2 (5 x^{6} - 1)

Evaluate

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

Multiply

More Steps

Evaluate

2 x^{3} \times 5 x^{2} \times x

Multiply the terms

10 x^{3} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{3 + 2 + 1}

Add the numbers

10 x^{6}

10 x^{6} - 2

Solution

2 (5 x^{6} - 1)

Show Solution

Find the roots

x_{1} = - \frac{6 3125}{5}, x_{2} = \frac{6 3125}{5}

Alternative Form

x_{1} \approx - 0.764724, x_{2} \approx 0.764724

Evaluate

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

To find the roots of the expression,set the expression equal to 0

2 x^{3} \times 5 x^{2} \times x - 2 = 0

Multiply

More Steps

Multiply the terms

2 x^{3} \times 5 x^{2} \times x

Multiply the terms

10 x^{3} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{3 + 2 + 1}

Add the numbers

10 x^{6}

10 x^{6} - 2 = 0

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

10 x^{6} = 0 + 2

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

10 x^{6} = 2

Divide both sides

\frac{10 x ^{6}}{10} = \frac{2}{10}

Divide the numbers

x^{6} = \frac{2}{10}

Cancel out the common factor 2

x^{6} = \frac{1}{5}

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

x = \pm 6 \frac{1}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{5}

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

\frac{6 1}{6 5}

Simplify the radical expression

\frac{1}{6 5}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

65 \times 6 5^{5}

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

6 5 \times 5^{5}

Calculate the product

6 5^{6}

Reduce the index of the radical and exponent with 6

5

\frac{6 3125}{5}

x = \pm \frac{6 3125}{5}

Separate the equation into 2 possible cases

x = \frac{6 3125}{5} x = - \frac{6 3125}{5}

Solution

x_{1} = - \frac{6 3125}{5}, x_{2} = \frac{6 3125}{5}

Alternative Form

x_{1} \approx - 0.764724, x_{2} \approx 0.764724

Show Solution