Problem: z2 - 40z + 340 <= 4
z2 - 40z + 336 <= 0
(z - 12)(z - 28) <= 0
There are three regions: the region from 12 to the left, the region from 12 through 28, and the region from 28 to the right.
Choosing a number in the region from 12 to the left:
-- I can choose any number: I'm going to choose 0 because it is easy to work with:
(z - 12)(z - 28) ---> (0 - 12)(0 - 28) = (-12)(-28) = 336
Since this answer is not <= 0, this region will not work.
Choosing a number in the region from 12 through 28; I'm going to choose 20:
(z - 12)(z - 28) ---> (20 - 12)(20 - 28) = (8)(-8) = -64
Since this answer is <= 0, this region will work.
Choosing a number in the region from 28 to the right; I'm going to choose 30:
(z - 12)(z - 28) ---> (30 - 12)(30 - 28) = (18)(2) = 36
Since this answer is not <= 0, this region will not work.
So the answer is: [12, 28]
Use square brackets because the problem has an 'equal-to' sign.