math
posted by Karen .
At the ruins of Caesarea, archaeologists discovered a huge hydraulic concrete block with a volume of 945 cubic meters. The block's dimensions are x meters high by 12x  15 meters long by 12x  21 meters wide. What is the height of the block?
I have no idea how to do this. Can someone please help me?

remember , volume = lwh
x(12x15)(12x21) = 945
simplifying a bit
x(3)(4x  5)(3)(4x7) = 945
x(4x5)(4x7) = 105
16x^3 48x^2 +35x  105=0
by grouping ...
16x^2(x  3) + 35(x3) = 0
(x3)(16x^2 + 35) = 0
x = 3 or x^2 = 35/16 , which is not real
so the only real solution is x = 3
so the block is 3 m high, 
How do you get 105?

I divided both sides by 9
945รท9=105
notice the (3)(3) is gone on the left side
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