Solve 3/4q 11 = 4q^37

Question

Solve the equation

q_{1} = - \frac{231}{28}, q_{2} = 0, q_{3} = \frac{231}{28}

Alternative Form

q_{1} \approx - 0.54281, q_{2} = 0, q_{3} \approx 0.54281

Evaluate

\frac{3}{4} q \times 11 = 4 q^{3} \times 7

Multiply the terms

More Steps

Evaluate

\frac{3}{4} \times 11

Multiply the numbers

\frac{3 \times 11}{4}

Multiply the numbers

\frac{33}{4}

\frac{33}{4} q = 4 q^{3} \times 7

Multiply the terms

\frac{33}{4} q = 28 q^{3}

Add or subtract both sides

\frac{33}{4} q - 28 q^{3} = 0

Factor the expression

q (\frac{33}{4} - 28 q^{2}) = 0

Separate the equation into 2 possible cases

q = 0 \frac{33}{4} - 28 q^{2} = 0

Solve the equation

More Steps

Evaluate

\frac{33}{4} - 28 q^{2} = 0

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

- 28 q^{2} = 0 - \frac{33}{4}

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

- 28 q^{2} = - \frac{33}{4}

Change the signs on both sides of the equation

28 q^{2} = \frac{33}{4}

Multiply by the reciprocal

28 q^{2} \times \frac{1}{28} = \frac{33}{4} \times \frac{1}{28}

Multiply

q^{2} = \frac{33}{4} \times \frac{1}{28}

Multiply

More Steps

Evaluate

\frac{33}{4} \times \frac{1}{28}

To multiply the fractions,multiply the numerators and denominators separately

\frac{33}{4 \times 28}

Multiply the numbers

\frac{33}{112}

q^{2} = \frac{33}{112}

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

q = \pm \frac{33}{112}

Simplify the expression

More Steps

Evaluate

\frac{33}{112}

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

\frac{33}{112}

Simplify the radical expression

\frac{33}{4 7}

Multiply by the Conjugate

\frac{33 \times 7}{4 7 \times 7}

Multiply the numbers

\frac{231}{4 7 \times 7}

Multiply the numbers

\frac{231}{28}

q = \pm \frac{231}{28}

Separate the equation into 2 possible cases

q = \frac{231}{28} q = - \frac{231}{28}

q = 0 q = \frac{231}{28} q = - \frac{231}{28}

Solution

q_{1} = - \frac{231}{28}, q_{2} = 0, q_{3} = \frac{231}{28}

Alternative Form

q_{1} \approx - 0.54281, q_{2} = 0, q_{3} \approx 0.54281

Show Solution