Solve 2d^2 9d^3 = 3d

Question

Solve the equation

d_{1} = - \frac{4 216}{6}, d_{2} = 0, d_{3} = \frac{4 216}{6}

Alternative Form

d_{1} \approx - 0.638943, d_{2} = 0, d_{3} \approx 0.638943

Evaluate

2 d^{2} \times 9 d^{3} = 3 d

Multiply

More Steps

Evaluate

2 d^{2} \times 9 d^{3}

Multiply the terms

18 d^{2} \times d^{3}

Multiply the terms with the same base by adding their exponents

18 d^{2 + 3}

Add the numbers

18 d^{5}

18 d^{5} = 3 d

Add or subtract both sides

18 d^{5} - 3 d = 0

Factor the expression

3 d (6 d^{4} - 1) = 0

Divide both sides

d (6 d^{4} - 1) = 0

Separate the equation into 2 possible cases

d = 0 6 d^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

6 d^{4} - 1 = 0

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

6 d^{4} = 0 + 1

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

6 d^{4} = 1

Divide both sides

\frac{6 d ^{4}}{6} = \frac{1}{6}

Divide the numbers

d^{4} = \frac{1}{6}

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

d = \pm 4 \frac{1}{6}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{6}

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

\frac{4 1}{4 6}

Simplify the radical expression

\frac{1}{4 6}

Multiply by the Conjugate

\frac{4 6 ^{3}}{4 6 \times 4 6 ^{3}}

Simplify

\frac{4 216}{4 6 \times 4 6 ^{3}}

Multiply the numbers

\frac{4 216}{6}

d = \pm \frac{4 216}{6}

Separate the equation into 2 possible cases

d = \frac{4 216}{6} d = - \frac{4 216}{6}

d = 0 d = \frac{4 216}{6} d = - \frac{4 216}{6}

Solution

d_{1} = - \frac{4 216}{6}, d_{2} = 0, d_{3} = \frac{4 216}{6}

Alternative Form

d_{1} \approx - 0.638943, d_{2} = 0, d_{3} \approx 0.638943

Show Solution