SOLUTION: you are given a cube. the length, width, and height = x. if the length is increased by 12, the width is increased by 6, and the height is decreased by 4 than the volume doubles. fi

Algebra ->  Trigonometry-basics -> SOLUTION: you are given a cube. the length, width, and height = x. if the length is increased by 12, the width is increased by 6, and the height is decreased by 4 than the volume doubles. fi      Log On


   

Question 177739: you are given a cube. the length, width, and height = x. if the length is increased by 12, the width is increased by 6, and the height is decreased by 4 than the volume doubles. find x.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
A=x%5E3....eq 1
:
%28x%2B12%29%28x%2B6%29%28x-4%29=2A...eq 2
:
take value of A from eq 1 and plug it into eq 2
:
%28x%2B12%29%28x%2B6%29%28x-4%29=2x%5E3
:
%28x%5E2%2B18x%2B72%29%28x-4%29=2x%5E3
:
x%5E3-4x%5E2%2B18x%5E2-72x%2B72x-288=2x%5E3
:
x%5E3-14x%5E2%2B288=0
if we take the factors of plus or minus 288/1 we have possible rational roots
:
if you plug 6 in you will find that to be a factor so lets use synthetic division to factor 6 out of our equation
:
:
l 1 -14 0 288
l
6 l____ 6___-48___-288____________________________
1 -8 -48 0
so we have (x-6)(x^2-8x-48)
which can be further factored to (x-6)(x-12)(x+4)
:
so x is 6,12,0r -4..since 4 is negative we throw it out
:
system%28x=6%2Cx=12%29