(x-3)2+6=0

Subtract 6 from both sides of the equation.

(x-3)2=-6

Take the square root of each side of the equation to set up the solution for x

(x-3)2⋅12=±-6

Remove the perfect root factor x-3 under the radical to solve for x.

x-3=±-6

Rewrite -6 as -1(6).

x-3=±-1⋅6

Rewrite -1(6) as -1⋅6.

x-3=±-1⋅6

Rewrite -1 as i.

x-3=±i6

x-3=±i6

First, use the positive value of the ± to find the first solution.

x-3=i6

Add 3 to both sides of the equation.

x=i6+3

Next, use the negative value of the ± to find the second solution.

x-3=-i6

Add 3 to both sides of the equation.

x=-i6+3

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

x=i6+3,-i6+3

x=i6+3,-i6+3

Solve Using the Square Root Property (x-3)^2+6=0