show how many solutions are in the solution set for 2(x-5)^2 + 2 = 20

Answer 1

To find the number of solutions in the solution set for the equation 2(x-5)^2 + 2 = 20, we first simplify the equation:

2(x-5)^2 + 2 = 20
2(x-5)^2 = 18
(x-5)^2 = 9
x-5 = ±√9

Now we solve for x:

x-5 = 3 or x-5 = -3

For x-5 = 3, we add 5 to both sides:
x-5+5 = 3+5
x = 8

For x-5 = -3, we add 5 to both sides:
x-5+5 = -3+5
x = 2

Thus, there are 2 solutions in the solution set for the equation 2(x-5)^2 + 2 = 20, which are x = 8 and x = 2.