Finite Math Examples

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

Step 1

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

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

Step 2

Solve for $x$ .

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Step 2.1

Add $2$ to both sides of the equation.

${(x + 1)}^{2} = 2$

Step 2.2

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

$x + 1 = \pm \sqrt{2}$

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.

$x + 1 = \sqrt{2}$

Step 2.3.2

Subtract $1$ from both sides of the equation.

$x = \sqrt{2} - 1$

Step 2.3.3

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

$x + 1 = - \sqrt{2}$

Step 2.3.4

Subtract $1$ from both sides of the equation.

$x = - \sqrt{2} - 1$

Step 2.3.5

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

$x = \sqrt{2} - 1, - \sqrt{2} - 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{2} - 1, - \sqrt{2} - 1$

Decimal Form:

$x = 0.41421356 \dots, - 2.41421356 \dots$

Step 4