Solve 3x^5x - 2x - ScanMath

Question

Simplify the expression

3 x^{6} - 2 x

Evaluate

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

Solution

More Steps

Evaluate

3 x^{5} \times x

Multiply the terms with the same base by adding their exponents

3 x^{5 + 1}

Add the numbers

3 x^{6}

3 x^{6} - 2 x

Show Solution

x (3 x^{5} - 2)

Evaluate

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

Multiply

More Steps

Evaluate

3 x^{5} \times x

Multiply the terms with the same base by adding their exponents

3 x^{5 + 1}

Add the numbers

3 x^{6}

3 x^{6} - 2 x

Rewrite the expression

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

Solution

x (3 x^{5} - 2)

Show Solution

x_{1} = 0, x_{2} = \frac{5 162}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.922108

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

3 x^{5} \times x

Multiply the terms with the same base by adding their exponents

3 x^{5 + 1}

Add the numbers

3 x^{6}

3 x^{6} - 2 x = 0

Factor the expression

x (3 x^{5} - 2) = 0

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

3 x^{5} - 2 = 0

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

3 x^{5} = 0 + 2

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

3 x^{5} = 2

Divide both sides

\frac{3 x ^{5}}{3} = \frac{2}{3}

Divide the numbers

x^{5} = \frac{2}{3}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{2}{3}

Calculate

x = 5 \frac{2}{3}

Simplify the root

More Steps

Evaluate

5 \frac{2}{3}

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

\frac{5 2}{5 3}

Multiply by the Conjugate

\frac{5 2 \times 5 3 ^{4}}{5 3 \times 5 3 ^{4}}

Simplify

\frac{5 2 \times 5 81}{5 3 \times 5 3 ^{4}}

Multiply the numbers

\frac{5 162}{5 3 \times 5 3 ^{4}}

Multiply the numbers

\frac{5 162}{3}

x = \frac{5 162}{3}

x = 0 x = \frac{5 162}{3}

Solution

x_{1} = 0, x_{2} = \frac{5 162}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 0.922108

Show Solution