Solve 4x^(2)(10x^(2) 3x-7)

Question

Simplify the expression

120 x^{5} - 28 x^{2}

Evaluate

4 x^{2} (10 x^{2} \times 3 x - 7)

Multiply

More Steps

Evaluate

10 x^{2} \times 3 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

4 x^{2} (30 x^{3} - 7)

Apply the distributive property

4 x^{2} \times 30 x^{3} - 4 x^{2} \times 7

Multiply the terms

More Steps

Evaluate

4 x^{2} \times 30 x^{3}

Multiply the numbers

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

Multiply the terms

More Steps

Evaluate

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

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

x^{2 + 3}

Add the numbers

x^{5}

120 x^{5}

120 x^{5} - 4 x^{2} \times 7

Solution

120 x^{5} - 28 x^{2}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 6300}{30}

Alternative Form

x_{1} = 0, x_{2} \approx 0.615638

Evaluate

4 x^{2} (10 x^{2} \times 3 x - 7)

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

4 x^{2} (10 x^{2} \times 3 x - 7) = 0

Multiply

More Steps

Multiply the terms

10 x^{2} \times 3 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

4 x^{2} (30 x^{3} - 7) = 0

Elimination the left coefficient

x^{2} (30 x^{3} - 7) = 0

Separate the equation into 2 possible cases

x^{2} = 0 30 x^{3} - 7 = 0

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

x = 0 30 x^{3} - 7 = 0

Solve the equation

More Steps

Evaluate

30 x^{3} - 7 = 0

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

30 x^{3} = 0 + 7

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

30 x^{3} = 7

Divide both sides

\frac{30 x ^{3}}{30} = \frac{7}{30}

Divide the numbers

x^{3} = \frac{7}{30}

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

3 x^{3} = 3 \frac{7}{30}

Calculate

x = 3 \frac{7}{30}

Simplify the root

More Steps

Evaluate

3 \frac{7}{30}

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

\frac{3 7}{3 30}

Multiply by the Conjugate

\frac{3 7 \times 3 3 0 ^{2}}{3 30 \times 3 3 0 ^{2}}

Simplify

\frac{3 7 \times 3 900}{3 30 \times 3 3 0 ^{2}}

Multiply the numbers

\frac{3 6300}{3 30 \times 3 3 0 ^{2}}

Multiply the numbers

\frac{3 6300}{30}

x = \frac{3 6300}{30}

x = 0 x = \frac{3 6300}{30}

Solution

x_{1} = 0, x_{2} = \frac{3 6300}{30}

Alternative Form

x_{1} = 0, x_{2} \approx 0.615638

Show Solution