Pre-Algebra Examples

${(x - 4)}^{2} - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

${(x - 4)}^{2} = 6$

Step 2

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

$x - 4 = \pm \sqrt{6}$

Step 3

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

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Step 3.1

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

$x - 4 = \sqrt{6}$

Step 3.2

Add $4$ to both sides of the equation.

$x = \sqrt{6} + 4$

Step 3.3

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

$x - 4 = - \sqrt{6}$

Step 3.4

Add $4$ to both sides of the equation.

$x = - \sqrt{6} + 4$

Step 3.5

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

$x = \sqrt{6} + 4, - \sqrt{6} + 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{6} + 4, - \sqrt{6} + 4$

Decimal Form:

$x = 6.44948974 \dots, 1.55051025 \dots$