Solve 4x 8x^3x -12x 18

Question

Simplify the expression

32 x^{5} - 216 x

Evaluate

4 x \times 8 x^{3} \times x - 12 x \times 18

Multiply

More Steps

Multiply the terms

4 x \times 8 x^{3} \times x

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

32 x^{1 + 3 + 1}

Add the numbers

32 x^{5}

32 x^{5} - 12 x \times 18

Solution

32 x^{5} - 216 x

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Factor the expression

8 x (4 x^{4} - 27)

Evaluate

4 x \times 8 x^{3} \times x - 12 x \times 18

Multiply

More Steps

Multiply the terms

4 x \times 8 x^{3} \times x

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

32 x^{1 + 3 + 1}

Add the numbers

32 x^{5}

32 x^{5} - 12 x \times 18

Multiply the terms

32 x^{5} - 216 x

Rewrite the expression

8 x \times 4 x^{4} - 8 x \times 27

Solution

8 x (4 x^{4} - 27)

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Find the roots

x_{1} = - \frac{4 108}{2}, x_{2} = 0, x_{3} = \frac{4 108}{2}

Alternative Form

x_{1} \approx - 1.611855, x_{2} = 0, x_{3} \approx 1.611855

Evaluate

4 x \times 8 x^{3} \times x - 12 x \times 18

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

4 x \times 8 x^{3} \times x - 12 x \times 18 = 0

Multiply

More Steps

Multiply the terms

4 x \times 8 x^{3} \times x

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

32 x^{1 + 3 + 1}

Add the numbers

32 x^{5}

32 x^{5} - 12 x \times 18 = 0

Multiply the terms

32 x^{5} - 216 x = 0

Factor the expression

8 x (4 x^{4} - 27) = 0

Divide both sides

x (4 x^{4} - 27) = 0

Separate the equation into 2 possible cases

x = 0 4 x^{4} - 27 = 0

Solve the equation

More Steps

Evaluate

4 x^{4} - 27 = 0

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

4 x^{4} = 0 + 27

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

4 x^{4} = 27

Divide both sides

\frac{4 x ^{4}}{4} = \frac{27}{4}

Divide the numbers

x^{4} = \frac{27}{4}

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

x = \pm 4 \frac{27}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{27}{4}

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

\frac{4 27}{4 4}

Simplify the radical expression

\frac{4 27}{2}

Multiply by the Conjugate

\frac{4 27 \times 2}{2 \times 2}

Multiply the numbers

\frac{4 108}{2 \times 2}

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

\frac{4 108}{2}

x = \pm \frac{4 108}{2}

Separate the equation into 2 possible cases

x = \frac{4 108}{2} x = - \frac{4 108}{2}

x = 0 x = \frac{4 108}{2} x = - \frac{4 108}{2}

Solution

x_{1} = - \frac{4 108}{2}, x_{2} = 0, x_{3} = \frac{4 108}{2}

Alternative Form

x_{1} \approx - 1.611855, x_{2} = 0, x_{3} \approx 1.611855

Show Solution