SOLUTION: 1/3x^2-3x+14 2/3=2x

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Question 153512: 1/3x^2-3x+14 2/3=2x
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to change the equation into the standard form.
%281%2F3%29x%5E2-3x%2B14%2B2%2F3=2x
%281%2F3%29x%5E2-3x%2B44%2F3=2x
3%28%281%2F3%29x%5E2-3x%2B44%2F3%29=3%2A2x (multiply both sides by 3)
x%5E2-9x%2B44=6x
x%5E2-15x%2B44=0
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SOLVED BY FACTORING
The left side of the equation can be factored as x%5E2-15x%2B44=%28x-4%29%28x-11%29.
So the equation becomes:
%28x-4%29%28x-11%29=0
so x= 4 or x = 11
SOLVED BY USING QUADRATIC FORMULA
Substituting
a = 1
b = -15
c = 44
into
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+, we have
x+=+%28-%28-15%29+%2B-+sqrt%28+%28-15%29%5E2-4%2A1%2A44+%29%29%2F%282%2A1%29+
x+=+%2815+%2B-+sqrt%28+225-176+%29%29%2F2+
x+=+%2815+%2B-+sqrt%28+49+%29%29%2F2+
x+=+%2815+%2B-+7%29%2F2+
So
x+=+%2815+%2B+7%29%2F2+=22%2F2+=+11
Or
x+=+%2815+-+7%29%2F2+=8%2F2+=+4