Luke has a crate with a volume of 2160 cubic inches. The crate is 12 inches long and 18 inches high. Luke wants to put wooden boards into the crate. Each board is the same size as the board shown in the diagram.
What is the greatest number of boards that will fit in the crate?

b

step-by-step explanation:

here's a poem i finished a while ago. i hope you like it and that it inspires you.

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0

to complete this square you have to rotate about the origin 270 degrees clockwise.