Solve 2/3 y 11 = 4y^31

Question

Solve the equation

y_{1} = - \frac{66}{6}, y_{2} = 0, y_{3} = \frac{66}{6}

Alternative Form

y_{1} \approx - 1.354006, y_{2} = 0, y_{3} \approx 1.354006

Evaluate

\frac{2}{3} y \times 11 = 4 y^{3} \times 1

Multiply the terms

More Steps

Evaluate

\frac{2}{3} \times 11

Multiply the numbers

\frac{2 \times 11}{3}

Multiply the numbers

\frac{22}{3}

\frac{22}{3} y = 4 y^{3} \times 1

Multiply the terms

\frac{22}{3} y = 4 y^{3}

Add or subtract both sides

\frac{22}{3} y - 4 y^{3} = 0

Factor the expression

y (\frac{22}{3} - 4 y^{2}) = 0

Separate the equation into 2 possible cases

y = 0 \frac{22}{3} - 4 y^{2} = 0

Solve the equation

More Steps

Evaluate

\frac{22}{3} - 4 y^{2} = 0

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

- 4 y^{2} = 0 - \frac{22}{3}

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

- 4 y^{2} = - \frac{22}{3}

Change the signs on both sides of the equation

4 y^{2} = \frac{22}{3}

Multiply by the reciprocal

4 y^{2} \times \frac{1}{4} = \frac{22}{3} \times \frac{1}{4}

Multiply

y^{2} = \frac{22}{3} \times \frac{1}{4}

Multiply

More Steps

Evaluate

\frac{22}{3} \times \frac{1}{4}

Reduce the numbers

\frac{11}{3} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{11}{3 \times 2}

Multiply the numbers

\frac{11}{6}

y^{2} = \frac{11}{6}

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

y = \pm \frac{11}{6}

Simplify the expression

More Steps

Evaluate

\frac{11}{6}

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

\frac{11}{6}

Multiply by the Conjugate

\frac{11 \times 6}{6 \times 6}

Multiply the numbers

\frac{66}{6 \times 6}

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

\frac{66}{6}

y = \pm \frac{66}{6}

Separate the equation into 2 possible cases

y = \frac{66}{6} y = - \frac{66}{6}

y = 0 y = \frac{66}{6} y = - \frac{66}{6}

Solution

y_{1} = - \frac{66}{6}, y_{2} = 0, y_{3} = \frac{66}{6}

Alternative Form

y_{1} \approx - 1.354006, y_{2} = 0, y_{3} \approx 1.354006

Show Solution