Solve 4x^4-32x^3 48x^2

Question

Simplify the expression

4 x^{4} - 1536 x^{5}

Evaluate

4 x^{4} - 32 x^{3} \times 48 x^{2}

Solution

More Steps

Evaluate

32 x^{3} \times 48 x^{2}

Multiply the terms

1536 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

1536 x^{3 + 2}

Add the numbers

1536 x^{5}

4 x^{4} - 1536 x^{5}

Show Solution

4 x^{4} (1 - 384 x)

Evaluate

4 x^{4} - 32 x^{3} \times 48 x^{2}

Multiply

More Steps

Evaluate

32 x^{3} \times 48 x^{2}

Multiply the terms

1536 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

1536 x^{3 + 2}

Add the numbers

1536 x^{5}

4 x^{4} - 1536 x^{5}

Rewrite the expression

4 x^{4} - 4 x^{4} \times 384 x

Solution

4 x^{4} (1 - 384 x)

Show Solution

x_{1} = 0, x_{2} = \frac{1}{384}

Alternative Form

x_{1} = 0, x_{2} \approx 0.002604

Evaluate

4 x^{4} - 32 x^{3} \times 48 x^{2}

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

4 x^{4} - 32 x^{3} \times 48 x^{2} = 0

Multiply

More Steps

Multiply the terms

32 x^{3} \times 48 x^{2}

Multiply the terms

1536 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

1536 x^{3 + 2}

Add the numbers

1536 x^{5}

4 x^{4} - 1536 x^{5} = 0

Factor the expression

4 x^{4} (1 - 384 x) = 0

Divide both sides

x^{4} (1 - 384 x) = 0

Separate the equation into 2 possible cases

x^{4} = 0 1 - 384 x = 0

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

x = 0 1 - 384 x = 0

Solve the equation

More Steps

Evaluate

1 - 384 x = 0

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

- 384 x = 0 - 1

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

- 384 x = - 1

Change the signs on both sides of the equation

384 x = 1

Divide both sides

\frac{384 x}{384} = \frac{1}{384}

Divide the numbers

x = \frac{1}{384}

x = 0 x = \frac{1}{384}

Solution

x_{1} = 0, x_{2} = \frac{1}{384}

Alternative Form

x_{1} = 0, x_{2} \approx 0.002604

Show Solution