Solve Using the Square Root Property (x-5)^2=1

${(x - 5)}^{2} = 1$

Step 1

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

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

Step 2

Any root of $1$ is $1$ .

$x - 5 = \pm 1$

Step 3

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.

$x - 5 = 1$

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

Add $5$ to both sides of the equation.

$x = 1 + 5$

Add $1$ and $5$ .

$x = 6$

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

$x - 5 = - 1$

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

Add $5$ to both sides of the equation.

$x = - 1 + 5$

Add $- 1$ and $5$ .

$x = 4$

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

$x = 6, 4$