Where did that add 40 subtract 40 come from in the end?

Module 2 Week 3 Day 10 Your Turn Explanation Part 2
Where did that add 40 subtract 40 come from in the end (around 8:15?)

Hi TSS Graviser,
That's a great question! What Prof. Loh did here is he came up with a pair of numbers that would satisfy both equations he wrote: \( \frac{a+b}{2} = 180 \) and \( ab = 80 \). The equation \( \frac{a+b}{2} = 180 \) represents the average, or the midpoint, between \( a \) and \( b \). Since the difference between the two numbers is 80, \( a \) and \( b \) should each be 40 degrees away from the average. And because \( a \) is greater than \( b \), 40 should be added to 180 (the average) for \( a \) and subtracted from 180 for \( b \). This gives us
\( a = 180+40 = 220 \) and \( b = 18040 = 140 \).
Please let us know if you are still confused!
Happy Learning,
The Daily Challenge Team 
why not 36 plus 44?

Hi again!
36 and 44 do add up to 80, which fulfills one of the equations given: \( ab = 80 \). Now, let's see if it satisfies the other equation, \( \frac{a+b}{2} = 180\). There are two possible cases:
 \( a = 180+36 = 216 \) and \( b = 18044 = 136 \)
 \( a = 180+44 = 224 \) and \( b = 18036 = 144 \)
(We are only adding numbers to \( a \) because it must be greater than \( b \).)
For the first case, the average (\( \frac{a+b}{2} \)) would be:
\( \frac{216+136}{2} = \frac{352}{2} = 176 \)For the second case, the average would be:
\( \frac{224+144}{2} = \frac{368}{2} = 184 \)Hence, when we use 36 and 44, it does not satisfy \( \frac{a+b}{2} = 180\). In fact, this is true for all pairs of numbers other than 36 and 44. I hope this helps!
Happy Learning,
The Daily Challenge Team