Solve 5/8 y-1 1/2 y^3

Question

Simplify the expression

\frac{5}{8} y - \frac{3}{2} y^{3}

Evaluate

\frac{5}{8} y - 1 \frac{1}{2} \times y^{3}

Solution

More Steps

Evaluate

1 \frac{1}{2}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{2 + 1}{2}

Add the terms

\frac{3}{2}

\frac{5}{8} y - \frac{3}{2} y^{3}

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Factor the expression

\frac{1}{8} y (5 - 12 y^{2})

Evaluate

\frac{5}{8} y - 1 \frac{1}{2} \times y^{3}

Covert the mixed number to an improper fraction

More Steps

Evaluate

1 \frac{1}{2}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{2 + 1}{2}

Add the terms

\frac{3}{2}

\frac{5}{8} y - \frac{3}{2} y^{3}

Rewrite the expression

\frac{1}{8} y \times 5 - \frac{1}{8} y \times 12 y^{2}

Solution

\frac{1}{8} y (5 - 12 y^{2})

Show Solution

Find the roots

y_{1} = - \frac{15}{6}, y_{2} = 0, y_{3} = \frac{15}{6}

Alternative Form

y_{1} \approx - 0.645497, y_{2} = 0, y_{3} \approx 0.645497

Evaluate

\frac{5}{8} y - 1 \frac{1}{2} \times y^{3}

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

\frac{5}{8} y - 1 \frac{1}{2} \times y^{3} = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

1 \frac{1}{2}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{2 + 1}{2}

Add the terms

\frac{3}{2}

\frac{5}{8} y - \frac{3}{2} y^{3} = 0

Factor the expression

y (\frac{5}{8} - \frac{3}{2} y^{2}) = 0

Separate the equation into 2 possible cases

y = 0 \frac{5}{8} - \frac{3}{2} y^{2} = 0

Solve the equation

More Steps

Evaluate

\frac{5}{8} - \frac{3}{2} y^{2} = 0

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

- \frac{3}{2} y^{2} = 0 - \frac{5}{8}

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

- \frac{3}{2} y^{2} = - \frac{5}{8}

Change the signs on both sides of the equation

\frac{3}{2} y^{2} = \frac{5}{8}

Multiply by the reciprocal

\frac{3}{2} y^{2} \times \frac{2}{3} = \frac{5}{8} \times \frac{2}{3}

Multiply

y^{2} = \frac{5}{8} \times \frac{2}{3}

Multiply

More Steps

Evaluate

\frac{5}{8} \times \frac{2}{3}

Reduce the numbers

\frac{5}{4} \times \frac{1}{3}

To multiply the fractions,multiply the numerators and denominators separately

\frac{5}{4 \times 3}

Multiply the numbers

\frac{5}{12}

y^{2} = \frac{5}{12}

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

y = \pm \frac{5}{12}

Simplify the expression

More Steps

Evaluate

\frac{5}{12}

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

\frac{5}{12}

Simplify the radical expression

\frac{5}{2 3}

Multiply by the Conjugate

\frac{5 \times 3}{2 3 \times 3}

Multiply the numbers

\frac{15}{2 3 \times 3}

Multiply the numbers

\frac{15}{6}

y = \pm \frac{15}{6}

Separate the equation into 2 possible cases

y = \frac{15}{6} y = - \frac{15}{6}

y = 0 y = \frac{15}{6} y = - \frac{15}{6}

Solution

y_{1} = - \frac{15}{6}, y_{2} = 0, y_{3} = \frac{15}{6}

Alternative Form

y_{1} \approx - 0.645497, y_{2} = 0, y_{3} \approx 0.645497

Show Solution