Solve 5n^2-20n^6=0

Question

Solve the equation

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

Alternative Form

n_{1} \approx - 0.707107, n_{2} = 0, n_{3} \approx 0.707107

Evaluate

5 n^{2} - 20 n^{6} = 0

Factor the expression

5 n^{2} (1 - 4 n^{4}) = 0

Divide both sides

n^{2} (1 - 4 n^{4}) = 0

Separate the equation into 2 possible cases

n^{2} = 0 1 - 4 n^{4} = 0

The only way a power can be 0 is when the base equals 0

n = 0 1 - 4 n^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 4 n^{4} = 0

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

- 4 n^{4} = 0 - 1

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

- 4 n^{4} = - 1

Change the signs on both sides of the equation

4 n^{4} = 1

Divide both sides

\frac{4 n ^{4}}{4} = \frac{1}{4}

Divide the numbers

n^{4} = \frac{1}{4}

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

n = \pm 4 \frac{1}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{4}

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

\frac{4 1}{4 4}

Simplify the radical expression

\frac{1}{4 4}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

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

\frac{2}{2}

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

Separate the equation into 2 possible cases

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

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

Solution

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

Alternative Form

n_{1} \approx - 0.707107, n_{2} = 0, n_{3} \approx 0.707107

Show Solution