Solve (2x^4)(5x^2 2x-3)

Question

Simplify the expression

20 x^{7} - 6 x^{4}

Evaluate

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

Multiply

More Steps

Evaluate

5 x^{2} \times 2 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

2 x^{4} (10 x^{3} - 3)

Apply the distributive property

2 x^{4} \times 10 x^{3} - 2 x^{4} \times 3

Multiply the terms

More Steps

Evaluate

2 x^{4} \times 10 x^{3}

Multiply the numbers

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

Multiply the terms

More Steps

Evaluate

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

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{4 + 3}

Add the numbers

x^{7}

20 x^{7}

20 x^{7} - 2 x^{4} \times 3

Solution

20 x^{7} - 6 x^{4}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 300}{10}

Alternative Form

x_{1} = 0, x_{2} \approx 0.669433

Evaluate

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

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

(2 x^{4}) (5 x^{2} \times 2 x - 3) = 0

Multiply the terms

2 x^{4} (5 x^{2} \times 2 x - 3) = 0

Multiply

More Steps

Multiply the terms

5 x^{2} \times 2 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

2 x^{4} (10 x^{3} - 3) = 0

Elimination the left coefficient

x^{4} (10 x^{3} - 3) = 0

Separate the equation into 2 possible cases

x^{4} = 0 10 x^{3} - 3 = 0

The only way a power can be 0 is when the base equals 0

x = 0 10 x^{3} - 3 = 0

Solve the equation

More Steps

Evaluate

10 x^{3} - 3 = 0

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

10 x^{3} = 0 + 3

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

10 x^{3} = 3

Divide both sides

\frac{10 x ^{3}}{10} = \frac{3}{10}

Divide the numbers

x^{3} = \frac{3}{10}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{3}{10}

Calculate

x = 3 \frac{3}{10}

Simplify the root

More Steps

Evaluate

3 \frac{3}{10}

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

\frac{3 3}{3 10}

Multiply by the Conjugate

\frac{3 3 \times 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{3 3 \times 3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

\frac{3 300}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

\frac{3 300}{10}

x = \frac{3 300}{10}

x = 0 x = \frac{3 300}{10}

Solution

x_{1} = 0, x_{2} = \frac{3 300}{10}

Alternative Form

x_{1} = 0, x_{2} \approx 0.669433

Show Solution