SOLUTION: Show that all values are positive for P=3xsquared-6x+12 The answer is 3(x-1)squared + 9 Please can you show steps

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Question 752885: Show that all values are positive for P=3xsquared-6x+12
The answer is 3(x-1)squared + 9
Please can you show steps
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
This is done by completing the square.
3x^2 - 6x + 12
Move the 12 to the right, leaving
the 3x^2 - 6x on the left
3x^2 - 6x +12
Take out 3 from 3x^2 -6x
3(x^2 - 2x) +12
The number in front of the x
halve and multiply by itself
-2 => -1 => -1^2 = 1
Place this at the end of
3(x^2 - 2x + 1) +12
Now (x^2 - 2x + 1) can be
converted to (x - 1)^2
So we have:
3(x - 1)^2
Now to balance placing the +1
in the left hand bracket we add
3 x -1 = -3 to the right hand
side.
This gives us:-
3(x - 1)^2 + 9
If there is a negative x placed in
the formula the square will convert
it to a positive value.
Hope this helps
:-)