SOLUTION: use factoring to solve the quadratic equation x(x-2)^3 - 35(x-2)^2 =0

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Question 513921: use factoring to solve the quadratic equation
x(x-2)^3 - 35(x-2)^2 =0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You really have a "quartic" (fourth power) equation here!
x%28x-2%29%5E3-35%28x-2%29%5E2+=+0 First, factor the common factor %28x-2%29%5E2
%28x-2%29%5E2%28x%28x-2%29-35%29+=+0 Simplify.
%28x-2%29%5E2%28x%5E2-2x-35%29+=+0 Apply the "zero product" rule.
%28x-2%29%5E2+=+0 or %28x%5E2-2x-35%29+=+0 so...
%28x-2%29%5E2+=+0
%28x-2%29%28x-2%29+=+0 and so x+=+2 x+=+2 a double root for this part!
x%5E2-2x-35+=+0 Factor.
%28x%2B5%29%28x-7%29+=+0 Apply the "zero product" rule.
x%2B5+=+0 or x-7+=+0 so...
x+=+-5 or x+=+7
The four roots are:
x+=+2, x+=+2, x+=+-5, x+=+7