Solve Using the Square Root Property (x-4)^2=5

${(x - 4)}^{2} = 5$

Step 1

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

$x - 4 = \pm \sqrt{5}$

Step 2

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.

$x - 4 = \sqrt{5}$

Add $4$ to both sides of the equation.

$x = \sqrt{5} + 4$

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

$x - 4 = - \sqrt{5}$

Add $4$ to both sides of the equation.

$x = - \sqrt{5} + 4$

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

$x = \sqrt{5} + 4, - \sqrt{5} + 4$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5} + 4, - \sqrt{5} + 4$

Decimal Form:

$x = 6.23606797 \dots, 1.76393202 \dots$