SOLUTION: Solve. |x²+6| = 5x

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Question 972335: Solve. |x²+6| = 5x
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x%5E2%2B6%29+=+5x...........by definition of abs value,abs%28x%5E2%2B6%29=x%5E2%2B6
x%5E2%2B6+=+5x
x%5E2+-5x%2B6=0
x%5E2-2x+-3x%2B6=0
%28x%5E2-2x%29-%283x-6%29=0
x%28x-2%29-3%28x-2%29=0
%28x-3%29%28x-2%29=0
solutions:
if %28x-3%29=0=>x=3
if %28x-2%29=0=>x=2


Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Solve. |x²+6| = 5x
Since x²+6 is always positive we do not need the absolute values,
however we must restrict the right side 5x to always be positive
too.  5x > 0, therefore x > 0

    |x²+6| = 5x   x > 0
      x²+6 = 5x
   x²-5x+6 = 0
(x-2)(x-3) = 0
x-2=0; x-3=0
  x=2;   x=3

They both came out positive so we do not need to say x > 0 or to
discard a solution.  Both are solutions:

Edwin