Solve for n n^4-49n^2=0

$n^{4} - 49 n^{2} = 0$

Factor the left side of the equation.

Rewrite $n^{4}$ as ${(n^{2})}^{2}$ .

${(n^{2})}^{2} - 49 n^{2} = 0$

Let $u = n^{2}$ . Substitute $u$ for all occurrences of $n^{2}$ .

$u^{2} - 49 u = 0$

Factor $u$ out of $u^{2} - 49 u$ .

Factor $u$ out of $u^{2}$ .

$u \cdot u - 49 u = 0$

Factor $u$ out of $- 49 u$ .

$u \cdot u + u \cdot - 49 = 0$

Factor $u$ out of $u \cdot u + u \cdot - 49$ .

$u (u - 49) = 0$

Replace all occurrences of $u$ with $n^{2}$ .

$n^{2} (n^{2} - 49) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$n^{2} = 0$

$n^{2} - 49 = 0$

Set $n^{2}$ equal to $0$ and solve for $n$ .

Set $n^{2}$ equal to $0$ .

$n^{2} = 0$

Solve $n^{2} = 0$ for $n$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$n = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$n = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$n = \pm 0$

Plus or minus $0$ is $0$ .

$n = 0$

Set $n^{2} - 49$ equal to $0$ and solve for $n$ .

Set $n^{2} - 49$ equal to $0$ .

$n^{2} - 49 = 0$

Solve $n^{2} - 49 = 0$ for $n$ .

Add $49$ to both sides of the equation.

$n^{2} = 49$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$n = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$n = \pm \sqrt{7^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$n = \pm 7$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$n = 7$

Next, use the negative value of the $\pm$ to find the second solution.

$n = - 7$

The complete solution is the result of both the positive and negative portions of the solution.

$n = 7, - 7$

The final solution is all the values that make $n^{2} (n^{2} - 49) = 0$ true.

$n = 0, 7, - 7$

Solve for n n^4-49n^2=0

Related Questions

Support LCMGCF.com by disabling your adblocker.