Solve 6n^3=4n 11 - ScanMath

Question

Solve the equation

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

Alternative Form

n_{1} \approx - 2.708013, n_{2} = 0, n_{3} \approx 2.708013

Evaluate

6 n^{3} = 4 n \times 11

Multiply the terms

6 n^{3} = 44 n

Add or subtract both sides

6 n^{3} - 44 n = 0

Factor the expression

2 n (3 n^{2} - 22) = 0

Divide both sides

n (3 n^{2} - 22) = 0

Separate the equation into 2 possible cases

n = 0 3 n^{2} - 22 = 0

Solve the equation

More Steps

Evaluate

3 n^{2} - 22 = 0

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

3 n^{2} = 0 + 22

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

3 n^{2} = 22

Divide both sides

\frac{3 n ^{2}}{3} = \frac{22}{3}

Divide the numbers

n^{2} = \frac{22}{3}

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

n = \pm \frac{22}{3}

Simplify the expression

More Steps

Evaluate

\frac{22}{3}

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

\frac{22}{3}

Multiply by the Conjugate

\frac{22 \times 3}{3 \times 3}

Multiply the numbers

\frac{66}{3 \times 3}

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

\frac{66}{3}

n = \pm \frac{66}{3}

Separate the equation into 2 possible cases

n = \frac{66}{3} n = - \frac{66}{3}

n = 0 n = \frac{66}{3} n = - \frac{66}{3}

Solution

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

Alternative Form

n_{1} \approx - 2.708013, n_{2} = 0, n_{3} \approx 2.708013

Show Solution