The answer is in the photo below
Answer:
The factors are ![7,(x-2),(x+4)](https://tex.z-dn.net/?f=7%2C%28x-2%29%2C%28x%2B4%29)
![7x^{2} +14x-56=7(x-2)(x+4)](https://tex.z-dn.net/?f=7x%5E%7B2%7D%20%2B14x-56%3D7%28x-2%29%28x%2B4%29)
Step-by-step explanation:
we have
![7x^{2} +14x-56](https://tex.z-dn.net/?f=7x%5E%7B2%7D%20%2B14x-56)
equate the expression to zero
![7x^{2} +14x-56=0](https://tex.z-dn.net/?f=7x%5E%7B2%7D%20%2B14x-56%3D0)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![7x^{2} +14x=56](https://tex.z-dn.net/?f=7x%5E%7B2%7D%20%2B14x%3D56)
Factor the leading coefficient
![7(x^{2} +2x)=56](https://tex.z-dn.net/?f=7%28x%5E%7B2%7D%20%2B2x%29%3D56)
![(x^{2} +2x)=8](https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20%2B2x%29%3D8)
Complete the square. Remember to balance the equation by adding the same constants to each side
![(x^{2} +2x+1)=8+1](https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20%2B2x%2B1%29%3D8%2B1)
![(x^{2} +2x+1)=9](https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20%2B2x%2B1%29%3D9)
Rewrite as perfect squares
![(x+1)^{2}=9](https://tex.z-dn.net/?f=%28x%2B1%29%5E%7B2%7D%3D9)
Take square root both sides
![(x+1)=(+/-)3](https://tex.z-dn.net/?f=%28x%2B1%29%3D%28%2B%2F-%293)
![x=-1(+/-)3](https://tex.z-dn.net/?f=x%3D-1%28%2B%2F-%293)
![x=-1(+)3=2](https://tex.z-dn.net/?f=x%3D-1%28%2B%293%3D2)
![x=-1(-)3=-4](https://tex.z-dn.net/?f=x%3D-1%28-%293%3D-4)
therefore
![7x^{2} +14x-56=7(x-2)(x+4)](https://tex.z-dn.net/?f=7x%5E%7B2%7D%20%2B14x-56%3D7%28x-2%29%28x%2B4%29)
You can use a protractor to solve for the angles
Define rates at which the individuals paint.
Bill: x = 1/8 signs/h
Bob: y = (2 signs)/(8 h) = 1/4 signs/h
Barry: z = (4/3 signs)/(8 h) = 1/6 signs/h
The job is to paint 2 signs, working together.
In the first 3 hours, the amount painted is
(x+y+z signs/h)*(3 h) = (1/8 + 1/4 + 1/6)*3 = 13/8 signs
Remaining: 2 - 13/8 = 3/8 signs
Barry quits.
In the next 1/2 hour (30 minutes), the amount painted is
(x + y signs/h)*(0.5 h) = (1/8 + 1/4)*0.5 = 3/16 signs
Remaining: 3/8 - 3/16 = 3/16 signs
Now Bob quits.
The time for Bill to finish the job is
(3/16 signs)/(1/8 signs/h) = 3/2 h
Answer: Bill finishes the job in 1.5 hours (or 1 hour, 30 minutes)