Solve Using the Square Root Property (x-1)^2=3

${(x - 1)}^{2} = 3$

Step 1

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

$x - 1 = \pm \sqrt{3}$

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.

$x - 1 = \sqrt{3}$

Add $1$ to both sides of the equation.

$x = \sqrt{3} + 1$

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

$x - 1 = - \sqrt{3}$

Add $1$ to both sides of the equation.

$x = - \sqrt{3} + 1$

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

$x = \sqrt{3} + 1, - \sqrt{3} + 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{3} + 1, - \sqrt{3} + 1$

Decimal Form:

$x = 2.73205080 \dots, - 0.73205080 \dots$