You can divide the whole expression by -3:
![-3x^2+24x=27 \iff x^2-8x = -9](https://tex.z-dn.net/?f=-3x%5E2%2B24x%3D27%20%5Ciff%20x%5E2-8x%20%3D%20-9)
Recalling that
![(x-a)^2=x^2-2ax+a^2](https://tex.z-dn.net/?f=%28x-a%29%5E2%3Dx%5E2-2ax%2Ba%5E2)
Let's compare the middle term:
![-8x = -2ax \iff a=4](https://tex.z-dn.net/?f=-8x%20%3D%20-2ax%20%5Ciff%20a%3D4)
So, we want to complete
![(x-4)^2 = x^2-8x+16](https://tex.z-dn.net/?f=%28x-4%29%5E2%20%3D%20x%5E2-8x%2B16)
Which differs from
by 16. So, if we add 16 to both sides, we have
![x^2-8x=-9 \iff x^2-8x+16=7 \iff (x-4)^2=7](https://tex.z-dn.net/?f=x%5E2-8x%3D-9%20%5Ciff%20x%5E2-8x%2B16%3D7%20%5Ciff%20%28x-4%29%5E2%3D7)
Answer:
31
Step-by-step explanation:
|-10 + 41| = 31
The absolute value of a number is ALWAYS positive.
I am joyous to assist you anytime.
Total number of ways to make a pair:
The first player can be any one of 7 . For each of those . . .
The opponent can be any one of the remaining 6 .
Total ways to make a pair = 7 x 6 = 42 ways .
BUT ... every pair can be made in two ways ... A vs B or B vs A .
So 42 'ways' make only (42/2) = 21 different pairs.
If every pair plays 2 matches, then (21 x 2) = <em><u>42 total matches</u></em> will be played.
Now, is that an elegant solution or what !
4/5 x55
=4/5*55/1
=(4*55)/(5*1)
=220/5
=44/1
=44