Answer:
x=6
Explanation:
x-2 = sqrt(28-2x)
Square each side
(x-2)^2 = (sqrt(28-2x))^2
(x-2)^2 = 28-2x
FOIL
x^2 -4x+4 = 28-2x
Subtract 28 from each side
x^2 -4x+4-28 = 28-2x-28
x^2 -4x-24=-2x
Add 2x to each side
x^2 -2x-24=-2x
x^2 -2x+2x-24=-2x+2x
x^2-2x-24 =0
Factor
(x-6)(x+4)=0
Using the zero product property
x=6 x=-4
Check for extraneous solutions
x=6
x-2 = sqrt(28-2x)
6-2 =sqrt(28-12)
4 = sqrt(16)
4=4
Solution
x=-4
x-2 = sqrt(28-2x)
-4-2 =sqrt(28+8)
-6 = sqrt(36)
-6=6
Not a solution