Precalculus Examples

$| x^{2} - 3 | = 2$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x^{2} - 3 = \pm 2$

Step 2

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

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Step 2.1

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

$x^{2} - 3 = 2$

Step 2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.2.1

Add $3$ to both sides of the equation.

$x^{2} = 2 + 3$

Step 2.2.2

Add $2$ and $3$ .

$x^{2} = 5$

Step 2.3

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

$x = \pm \sqrt{5}$

Step 2.4

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

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Step 2.4.1

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

$x = \sqrt{5}$

Step 2.4.2

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

$x = - \sqrt{5}$

Step 2.4.3

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

$x = \sqrt{5}, - \sqrt{5}$

Step 2.5

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

$x^{2} - 3 = - 2$

Step 2.6

Move all terms not containing $x$ to the right side of the equation.

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Step 2.6.1

Add $3$ to both sides of the equation.

$x^{2} = - 2 + 3$

Step 2.6.2

Add $- 2$ and $3$ .

$x^{2} = 1$

Step 2.7

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

$x = \pm \sqrt{1}$

Step 2.8

Any root of $1$ is $1$ .

$x = \pm 1$

Step 2.9

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

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Step 2.9.1

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

$x = 1$

Step 2.9.2

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

$x = - 1$

Step 2.9.3

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

$x = 1, - 1$

Step 2.10

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

$x = \sqrt{5}, - \sqrt{5}, 1, - 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5}, - \sqrt{5}, 1, - 1$

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots, 1, - 1$