Algebra Examples

$y = x^{2} - 2$

Step 1

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

$x^{2} - 2 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $2$ to both sides of the equation.

$x^{2} = 2$

Step 2.2

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

$x = \pm \sqrt{2}$

Step 2.3

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

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Step 2.3.1

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

$x = \sqrt{2}$

Step 2.3.2

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

$x = - \sqrt{2}$

Step 2.3.3

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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

Step 4