Solve for x (x^2-100)(x^2+1)=0

$(x^{2} - 100) (x^{2} + 1) = 0$

Step 1

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

$x^{2} - 100 = 0$

$x^{2} + 1 = 0$

Step 2

Set $x^{2} - 100$ equal to $0$ and solve for $x$ .

Set $x^{2} - 100$ equal to $0$ .

$x^{2} - 100 = 0$

Solve $x^{2} - 100 = 0$ for $x$ .

Add $100$ to both sides of the equation.

$x^{2} = 100$

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

$x = \pm \sqrt{100}$

Simplify $\pm \sqrt{100}$ .

Rewrite $100$ as $10^{2}$ .

$x = \pm \sqrt{10^{2}}$

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

$x = \pm 10$

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.

$x = 10$

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

$x = - 10$

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

$x = 10, - 10$

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 $(x^{2} - 100) (x^{2} + 1) = 0$ true.

$x = 10, - 10, i, - i$

Solve for x (x^2-100)(x^2+1)=0

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