Solve Using the Square Root Property (x-3)^2=10

${(x - 3)}^{2} = 10$

Step 1

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

$x - 3 = \pm \sqrt{10}$

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.

$x - 3 = \sqrt{10}$

Add $3$ to both sides of the equation.

$x = \sqrt{10} + 3$

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

$x - 3 = - \sqrt{10}$

Add $3$ to both sides of the equation.

$x = - \sqrt{10} + 3$

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

$x = \sqrt{10} + 3, - \sqrt{10} + 3$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{10} + 3, - \sqrt{10} + 3$

Decimal Form:

$x = 6.16227766 \dots, - 0.16227766 \dots$