Solve 0=16x^3 165x^2-42x

Question

Solve the equation

x_{1} = - \frac{4 7 \times 44 0 ^{3}}{440}, x_{2} = 0, x_{3} = \frac{4 7 \times 44 0 ^{3}}{440}

Alternative Form

x_{1} \approx - 0.35515, x_{2} = 0, x_{3} \approx 0.35515

Evaluate

0 = 16 x^{3} \times 165 x^{2} - 42 x

Multiply

More Steps

Evaluate

16 x^{3} \times 165 x^{2}

Multiply the terms

2640 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

2640 x^{3 + 2}

Add the numbers

2640 x^{5}

0 = 2640 x^{5} - 42 x

Swap the sides of the equation

2640 x^{5} - 42 x = 0

Factor the expression

6 x (440 x^{4} - 7) = 0

Divide both sides

x (440 x^{4} - 7) = 0

Separate the equation into 2 possible cases

x = 0 440 x^{4} - 7 = 0

Solve the equation

More Steps

Evaluate

440 x^{4} - 7 = 0

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

440 x^{4} = 0 + 7

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

440 x^{4} = 7

Divide both sides

\frac{440 x ^{4}}{440} = \frac{7}{440}

Divide the numbers

x^{4} = \frac{7}{440}

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

x = \pm 4 \frac{7}{440}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{440}

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

\frac{4 7}{4 440}

Multiply by the Conjugate

\frac{4 7 \times 4 44 0 ^{3}}{4 440 \times 4 44 0 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 7 \times 44 0 ^{3}}{4 440 \times 4 44 0 ^{3}}

Multiply the numbers

\frac{4 7 \times 44 0 ^{3}}{440}

x = \pm \frac{4 7 \times 44 0 ^{3}}{440}

Separate the equation into 2 possible cases

x = \frac{4 7 \times 44 0 ^{3}}{440} x = - \frac{4 7 \times 44 0 ^{3}}{440}

x = 0 x = \frac{4 7 \times 44 0 ^{3}}{440} x = - \frac{4 7 \times 44 0 ^{3}}{440}

Solution

x_{1} = - \frac{4 7 \times 44 0 ^{3}}{440}, x_{2} = 0, x_{3} = \frac{4 7 \times 44 0 ^{3}}{440}

Alternative Form

x_{1} \approx - 0.35515, x_{2} = 0, x_{3} \approx 0.35515

Show Solution