Solve 4x^3-11x^2 2x^3

Question

Simplify the expression

4 x^{3} - 22 x^{5}

Evaluate

4 x^{3} - 11 x^{2} \times 2 x^{3}

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

22 x^{2 + 3}

Add the numbers

22 x^{5}

4 x^{3} - 22 x^{5}

Show Solution

Factor the expression

2 x^{3} (2 - 11 x^{2})

Evaluate

4 x^{3} - 11 x^{2} \times 2 x^{3}

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

22 x^{2 + 3}

Add the numbers

22 x^{5}

4 x^{3} - 22 x^{5}

Rewrite the expression

2 x^{3} \times 2 - 2 x^{3} \times 11 x^{2}

Solution

2 x^{3} (2 - 11 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{22}{11}, x_{2} = 0, x_{3} = \frac{22}{11}

Alternative Form

x_{1} \approx - 0.426401, x_{2} = 0, x_{3} \approx 0.426401

Evaluate

4 x^{3} - 11 x^{2} \times 2 x^{3}

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

4 x^{3} - 11 x^{2} \times 2 x^{3} = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

22 x^{2 + 3}

Add the numbers

22 x^{5}

4 x^{3} - 22 x^{5} = 0

Factor the expression

2 x^{3} (2 - 11 x^{2}) = 0

Divide both sides

x^{3} (2 - 11 x^{2}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 2 - 11 x^{2} = 0

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

x = 0 2 - 11 x^{2} = 0

Solve the equation

More Steps

Evaluate

2 - 11 x^{2} = 0

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

- 11 x^{2} = 0 - 2

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

- 11 x^{2} = - 2

Change the signs on both sides of the equation

11 x^{2} = 2

Divide both sides

\frac{11 x ^{2}}{11} = \frac{2}{11}

Divide the numbers

x^{2} = \frac{2}{11}

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

x = \pm \frac{2}{11}

Simplify the expression

More Steps

Evaluate

\frac{2}{11}

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

\frac{2}{11}

Multiply by the Conjugate

\frac{2 \times 11}{11 \times 11}

Multiply the numbers

\frac{22}{11 \times 11}

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

\frac{22}{11}

x = \pm \frac{22}{11}

Separate the equation into 2 possible cases

x = \frac{22}{11} x = - \frac{22}{11}

x = 0 x = \frac{22}{11} x = - \frac{22}{11}

Solution

x_{1} = - \frac{22}{11}, x_{2} = 0, x_{3} = \frac{22}{11}

Alternative Form

x_{1} \approx - 0.426401, x_{2} = 0, x_{3} \approx 0.426401

Show Solution