Solve for x (x^2-13)(x^2+1)=0

$(x^{2} - 13) (x^{2} + 1) = 0$

Step 1

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

$x^{2} - 13 = 0$

$x^{2} + 1 = 0$

Step 2

Set $x^{2} - 13$ equal to $0$ and solve for $x$ .

Set $x^{2} - 13$ equal to $0$ .

$x^{2} - 13 = 0$

Solve $x^{2} - 13 = 0$ for $x$ .

Add $13$ to both sides of the equation.

$x^{2} = 13$

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

$x = \pm \sqrt{13}$

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.

$x = \sqrt{13}$

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

$x = - \sqrt{13}$

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

$x = \sqrt{13}, - \sqrt{13}$

Step 3

Set $x^{2} + 1$ equal to $0$ and solve for $x$ .

Set $x^{2} + 1$ equal to $0$ .

$x^{2} + 1 = 0$

Solve $x^{2} + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$x^{2} = - 1$

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

$x = \pm \sqrt{- 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i$

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.

$x = i$

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

$x = - i$

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

$x = i, - i$

Step 4

The final solution is all the values that make $(x^{2} - 13) (x^{2} + 1) = 0$ true.

$x = \sqrt{13}, - \sqrt{13}, i, - i$