Solve for x -x^2-1=0

$- x^{2} - 1 = 0$

Step 1

Add $1$ to both sides of the equation.

$- x^{2} = 1$

Step 2

Divide each term in $- x^{2} = 1$ by $- 1$ and simplify.

Divide each term in $- x^{2} = 1$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{1}{- 1}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{1}{- 1}$

Simplify the right side.

Divide $1$ by $- 1$ .

$x^{2} = - 1$

Step 3

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

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

Step 4

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

$x = \pm i$

Step 5

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.

$x = i, - i$