Solve 4x^2 - 9x^596

Question

Simplify the expression

4 x^{2} - 864 x^{5}

Evaluate

4 x^{2} - 9 x^{5} \times 96

Solution

4 x^{2} - 864 x^{5}

Show Solution

4 x^{2} (1 - 6 x) (1 + 6 x + 36 x^{2})

Evaluate

4 x^{2} - 9 x^{5} \times 96

Evaluate

4 x^{2} - 864 x^{5}

Factor out 4 x^{2} from the expression

4 x^{2} (1 - 216 x^{3})

Solution

More Steps

Evaluate

1 - 216 x^{3}

Rewrite the expression in exponential form

1^{3} - (6 x)^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(1 - 6 x) (1^{2} + 1 \times 6 x + (6 x)^{2})

1 raised to any power equals to 1

(1 - 6 x) (1 + 1 \times 6 x + (6 x)^{2})

Any expression multiplied by 1 remains the same

(1 - 6 x) (1 + 6 x + (6 x)^{2})

Evaluate

More Steps

Evaluate

(6 x)^{2}

To raise a product to a power,raise each factor to that power

6^{2} x^{2}

Evaluate the power

36 x^{2}

(1 - 6 x) (1 + 6 x + 36 x^{2})

4 x^{2} (1 - 6 x) (1 + 6 x + 36 x^{2})

Show Solution

x_{1} = 0, x_{2} = \frac{1}{6}

Alternative Form

x_{1} = 0, x_{2} = 0.1 \dot{6}

Evaluate

4 x^{2} - 9 x^{5} \times 96

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

4 x^{2} - 9 x^{5} \times 96 = 0

Multiply the terms

4 x^{2} - 864 x^{5} = 0

Factor the expression

4 x^{2} (1 - 216 x^{3}) = 0

Divide both sides

x^{2} (1 - 216 x^{3}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 216 x^{3} = 0

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

x = 0 1 - 216 x^{3} = 0

Solve the equation

More Steps

Evaluate

1 - 216 x^{3} = 0

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

- 216 x^{3} = 0 - 1

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

- 216 x^{3} = - 1

Change the signs on both sides of the equation

216 x^{3} = 1

Divide both sides

\frac{216 x ^{3}}{216} = \frac{1}{216}

Divide the numbers

x^{3} = \frac{1}{216}

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

3 x^{3} = 3 \frac{1}{216}

Calculate

x = 3 \frac{1}{216}

Simplify the root

More Steps

Evaluate

3 \frac{1}{216}

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

\frac{3 1}{3 216}

Simplify the radical expression

\frac{1}{3 216}

Simplify the radical expression

\frac{1}{6}

x = \frac{1}{6}

x = 0 x = \frac{1}{6}

Solution

x_{1} = 0, x_{2} = \frac{1}{6}

Alternative Form

x_{1} = 0, x_{2} = 0.1 \dot{6}

Show Solution