Solve (4x^3-25)(4x-1x)

Question

Simplify the expression

12 x^{4} - 75 x

Evaluate

(4 x^{3} - 25) (4 x - 1 \times x)

Any expression multiplied by 1 remains the same

(4 x^{3} - 25) (4 x - x)

Subtract the terms

More Steps

Simplify

4 x - x

Collect like terms by calculating the sum or difference of their coefficients

(4 - 1) x

Subtract the numbers

3 x

(4 x^{3} - 25) \times 3 x

Multiply the terms

3 x (4 x^{3} - 25)

Apply the distributive property

3 x \times 4 x^{3} - 3 x \times 25

Multiply the terms

More Steps

Evaluate

3 x \times 4 x^{3}

Multiply the numbers

12 x \times x^{3}

Multiply the terms

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Evaluate

x \times x^{3}

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

x^{1 + 3}

Add the numbers

x^{4}

12 x^{4}

12 x^{4} - 3 x \times 25

Solution

12 x^{4} - 75 x

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 50}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.842016

Evaluate

(4 x^{3} - 25) (4 x - 1 \times x)

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

(4 x^{3} - 25) (4 x - 1 \times x) = 0

Any expression multiplied by 1 remains the same

(4 x^{3} - 25) (4 x - x) = 0

Subtract the terms

More Steps

Simplify

4 x - x

Collect like terms by calculating the sum or difference of their coefficients

(4 - 1) x

Subtract the numbers

3 x

(4 x^{3} - 25) \times 3 x = 0

Multiply the terms

3 x (4 x^{3} - 25) = 0

Elimination the left coefficient

x (4 x^{3} - 25) = 0

Separate the equation into 2 possible cases

x = 0 4 x^{3} - 25 = 0

Solve the equation

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Evaluate

4 x^{3} - 25 = 0

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

4 x^{3} = 0 + 25

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

4 x^{3} = 25

Divide both sides

\frac{4 x ^{3}}{4} = \frac{25}{4}

Divide the numbers

x^{3} = \frac{25}{4}

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

3 x^{3} = 3 \frac{25}{4}

Calculate

x = 3 \frac{25}{4}

Simplify the root

More Steps

Evaluate

3 \frac{25}{4}

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

\frac{3 25}{3 4}

Multiply by the Conjugate

\frac{3 25 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{3 25 \times 2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

\frac{2 3 50}{3 4 \times 3 4 ^{2}}

Multiply the numbers

\frac{2 3 50}{2 ^{2}}

Reduce the fraction

\frac{3 50}{2}

x = \frac{3 50}{2}

x = 0 x = \frac{3 50}{2}

Solution

x_{1} = 0, x_{2} = \frac{3 50}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.842016

Show Solution