Solve for x 2-x^2=0

$2 - x^{2} = 0$

Step 1

Subtract $2$ from both sides of the equation.

$- x^{2} = - 2$

Step 2

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

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

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

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x^{2} = 2$

Step 3

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

$x = \pm \sqrt{2}$

Step 4

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.

$x = \sqrt{2}$

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

$x = - \sqrt{2}$

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

$x = \sqrt{2}, - \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{2}, - \sqrt{2}$

Decimal Form:

$x = 1.41421356 \dots, - 1.41421356 \dots$