document.write( "Question 752885: Show that all values are positive for P=3xsquared-6x+12\r
\n" ); document.write( "\n" ); document.write( "The answer is 3(x-1)squared + 9\r
\n" ); document.write( "\n" ); document.write( "Please can you show steps \n" ); document.write( "
Algebra.Com's Answer #458152 by Cromlix(4381)\"\" \"About 
You can put this solution on YOUR website!
This is done by completing the square.
\n" ); document.write( " 3x^2 - 6x + 12
\n" ); document.write( "Move the 12 to the right, leaving
\n" ); document.write( "the 3x^2 - 6x on the left\r
\n" ); document.write( "\n" ); document.write( " 3x^2 - 6x +12
\n" ); document.write( "Take out 3 from 3x^2 -6x\r
\n" ); document.write( "\n" ); document.write( " 3(x^2 - 2x) +12
\n" ); document.write( "The number in front of the x
\n" ); document.write( "halve and multiply by itself\r
\n" ); document.write( "\n" ); document.write( " -2 => -1 => -1^2 = 1
\n" ); document.write( "Place this at the end of
\n" ); document.write( "3(x^2 - 2x + 1) +12\r
\n" ); document.write( "\n" ); document.write( "Now (x^2 - 2x + 1) can be
\n" ); document.write( "converted to (x - 1)^2\r
\n" ); document.write( "\n" ); document.write( "So we have:
\n" ); document.write( "3(x - 1)^2 \r
\n" ); document.write( "\n" ); document.write( "Now to balance placing the +1
\n" ); document.write( "in the left hand bracket we add
\n" ); document.write( "3 x -1 = -3 to the right hand
\n" ); document.write( "side.
\n" ); document.write( "This gives us:-
\n" ); document.write( "3(x - 1)^2 + 9
\n" ); document.write( "If there is a negative x placed in
\n" ); document.write( "the formula the square will convert
\n" ); document.write( "it to a positive value.
\n" ); document.write( "Hope this helps
\n" ); document.write( ":-) \n" ); document.write( "
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