Solve (22n)=2(2n) n^2

Question

Solve the equation

n_{1} = - \frac{22}{2}, n_{2} = 0, n_{3} = \frac{22}{2}

Alternative Form

n_{1} \approx - 2.345208, n_{2} = 0, n_{3} \approx 2.345208

Evaluate

22 n = 2 \times 2 n \times n^{2}

Multiply

More Steps

Evaluate

2 \times 2 n \times n^{2}

Multiply the terms

4 n \times n^{2}

Multiply the terms with the same base by adding their exponents

4 n^{1 + 2}

Add the numbers

4 n^{3}

22 n = 4 n^{3}

Add or subtract both sides

22 n - 4 n^{3} = 0

Factor the expression

2 n (11 - 2 n^{2}) = 0

Divide both sides

n (11 - 2 n^{2}) = 0

Separate the equation into 2 possible cases

n = 0 11 - 2 n^{2} = 0

Solve the equation

More Steps

Evaluate

11 - 2 n^{2} = 0

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

- 2 n^{2} = 0 - 11

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

- 2 n^{2} = - 11

Change the signs on both sides of the equation

2 n^{2} = 11

Divide both sides

\frac{2 n ^{2}}{2} = \frac{11}{2}

Divide the numbers

n^{2} = \frac{11}{2}

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

n = \pm \frac{11}{2}

Simplify the expression

More Steps

Evaluate

\frac{11}{2}

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

\frac{11}{2}

Multiply by the Conjugate

\frac{11 \times 2}{2 \times 2}

Multiply the numbers

\frac{22}{2 \times 2}

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

\frac{22}{2}

n = \pm \frac{22}{2}

Separate the equation into 2 possible cases

n = \frac{22}{2} n = - \frac{22}{2}

n = 0 n = \frac{22}{2} n = - \frac{22}{2}

Solution

n_{1} = - \frac{22}{2}, n_{2} = 0, n_{3} = \frac{22}{2}

Alternative Form

n_{1} \approx - 2.345208, n_{2} = 0, n_{3} \approx 2.345208

Show Solution