SOLUTION: |x-5|=7-2x

Algebra ->  Square-cubic-other-roots -> SOLUTION: |x-5|=7-2x      Log On


   

Question 812693: |x-5|=7-2x
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
What if you show the equation as sqrt%28%28x-5%29%5E2%29=7-2x ?
Square both sides:
%28x-5%29%5E2=49-28x%2B4x%5E2
x%5E2-10x%2B25=4x%5E2-28x%2B49
-10x%2B25=3x%5E2-28x%2B49
25=3x%5E2-18x%2B49
3x%5E2-18x%2B49-25=0
3x%5E2-18x%2B24=0 then divide all by 3.
x%5E2-6x%2B8=0

*Use general solution to quadratic formula; the quadratic appears nonfactorable.
discrimt is 36-4*8=4
square root of 4 is 2.

x=%286-2%29%2F2 or x=%286%2B2%29%2F2
x=2 or x=4


--------------------------
*The quadratic actually IS FACTORABLE.
%28x-2%29%28x-4%29
x%5E2-2x-4x%2B8
x%5E2-6x%2B8