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

Question

Simplify the expression

4 x^{3} - 20 - 3 x^{5} + 15 x^{2}

Evaluate

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

Multiply the terms

More Steps

Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

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

Apply the distributive property

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

Multiply the numbers

4 x^{3} - 20 - 3 x^{2} \times x^{3} - (- 3 x^{2} \times 5)

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}

4 x^{3} - 20 - 3 x^{5} - (- 3 x^{2} \times 5)

Multiply the numbers

4 x^{3} - 20 - 3 x^{5} - (- 15 x^{2})

Solution

4 x^{3} - 20 - 3 x^{5} + 15 x^{2}

Show Solution

Find the roots

x_{1} = - \frac{2 3}{3}, x_{2} = \frac{2 3}{3}, x_{3} = 35

Alternative Form

x_{1} \approx - 1.154701, x_{2} \approx 1.154701, x_{3} \approx 1.709976

Evaluate

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

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

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

Multiply the terms

More Steps

Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

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

Separate the equation into 2 possible cases

4 - 3 x^{2} = 0 x^{3} - 5 = 0

Solve the equation

More Steps

Evaluate

4 - 3 x^{2} = 0

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

- 3 x^{2} = 0 - 4

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

- 3 x^{2} = - 4

Change the signs on both sides of the equation

3 x^{2} = 4

Divide both sides

\frac{3 x ^{2}}{3} = \frac{4}{3}

Divide the numbers

x^{2} = \frac{4}{3}

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

x = \pm \frac{4}{3}

Simplify the expression

More Steps

Evaluate

\frac{4}{3}

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

\frac{4}{3}

Simplify the radical expression

\frac{2}{3}

Multiply by the Conjugate

\frac{2 3}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2 3}{3}

x = \pm \frac{2 3}{3}

Separate the equation into 2 possible cases

x = \frac{2 3}{3} x = - \frac{2 3}{3}

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

Solve the equation

More Steps

Evaluate

x^{3} - 5 = 0

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

x^{3} = 0 + 5

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

x^{3} = 5

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

3 x^{3} = 35

Calculate

x = 35

x = \frac{2 3}{3} x = - \frac{2 3}{3} x = 35

Solution

x_{1} = - \frac{2 3}{3}, x_{2} = \frac{2 3}{3}, x_{3} = 35

Alternative Form

x_{1} \approx - 1.154701, x_{2} \approx 1.154701, x_{3} \approx 1.709976

Show Solution