His friends ate 1/2 of 3/4..." of " means multiply
1/2 * 3/4 = 3/8
so his friends ate 3/8 of the bag of popcorn
X + y = 15
xy = -312
x + y = 15
x - x + y = -x + 15
y = -x + 15
xy = -312
x(-x + 15) = -312
x(-x) + x(15) = -312
-x² + 15x = -312
-x² + 15x + 312 = 0
-1(x²) - 1(-15x) - 1(312) = 0
-1(x² - 15x + 312) = 0
-1 -1
x² - 15x + 312 = 0
x = -(-15) ± √((-15)² - 4(1)(312))
2(1)
x = 15 ± √(225 - 1248)
2
x = 15 ± √(-1023)
2
x = 15 ± 31.984i
2
x = 7.5 ± 15.992
x = 7.5 + 15.992 or x = 7.5 - 15.992
x = 23.492 or x = -8.492
x + y = 15
23.492 + y = 15
- 23.492 - 23.492
y = -8.492
(x, y) = (23.492, -8.492)
or
x + y = 15
-8.492 + y = 15
+ 8.492 + 8.492
y = 23.492
(x, y) = (-8.492, 23.492)
The two numbers that add up to 15 and mutliply to -312 are -8.492 and 23.492.
Yeah that is correct so yeah you are right I don’t know any more information that I could give you but I’m pretty sure you just said it right so yeah
First see you can factor out 4. What is left is x^2 + 6x - 16.
That can be factored as (x+8)(x-2) so the total factorization is
4(x+8)(x-2)
