(x-5)2+10=4

Subtract 10 from both sides of the equation.

(x-5)2=4-10

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

(x-5)2⋅12=±4-10

Remove the perfect root factor x-5 under the radical to solve for x.

x-5=±4-10

Subtract 10 from 4.

x-5=±-6

Rewrite -6 as -1(6).

x-5=±-1⋅6

Rewrite -1(6) as -1⋅6.

x-5=±-1⋅6

Rewrite -1 as i.

x-5=±i6

x-5=±i6

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

x-5=i6

Add 5 to both sides of the equation.

x=i6+5

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

x-5=-i6

Add 5 to both sides of the equation.

x=-i6+5

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

x=i6+5,-i6+5

x=i6+5,-i6+5

Solve using the Square Root Property (x-5)^2+10=4