document.write( "Question 663432: My teacher put this problem and solution on the board and I need a laymans termed explaination of why he did certain things in the solution.\r
\n" ); document.write( "\n" ); document.write( "3x^2+4y^2-6x-24y+39=0
\n" ); document.write( "3(x^2-2x+1)+4(y^2-6y+1)=0-39+3+36
\n" ); document.write( "3(x-1)^2+4(y-3)^2=0\r
\n" ); document.write( "\n" ); document.write( "So, I get confused when my teacher added 1 inside both of the parenthesis...why did he do that? Where did he get the 1 from? Why not just leave the 1 out of both of the parenthesis? Please help! \n" ); document.write( "
Algebra.Com's Answer #412773 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
My teacher put this problem and solution on the board and I need a laymans termed explaination of why he did certain things in the solution.\r
\n" ); document.write( "\n" ); document.write( "3x^2+4y^2-6x-24y+39=0
\n" ); document.write( "3(x^2-2x+1)+4(y^2-6y+1)=0-39+3+36
\n" ); document.write( "3(x-1)^2+4(y-3)^2=0\r
\n" ); document.write( "\n" ); document.write( "So, I get confused when my teacher added 1 inside both of the parenthesis...why did he do that? Where did he get the 1 from? Why not just leave the 1 out of both of the parenthesis?
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\n" ); document.write( "3x^2+4y^2-6x-24y+39=0
\n" ); document.write( "He completed the squares of the x & y terms.
\n" ); document.write( "3x^2+4y^2-6x-24y+39=0
\n" ); document.write( "3x^2 - 6x + 4y^2 - 24y = -39
\n" ); document.write( "3(x^2 + 2x) + 4(y^2 - 6y) = -39
\n" ); document.write( "3(x^2 + 2x + 1) + 4(y^2 - 6y + 9) = -39 + 3*1 + 4*9 = 0
\n" ); document.write( "3(x+1)^2 + 4(y-3)^2 = 0
\n" ); document.write( "Divide by 3*4 = 12
\n" ); document.write( "(x+1)^2/4 + (y-3)^2/3 = 0
\n" ); document.write( "That's the standard form of an ellipse, but the right side = 0, so it's a \"point ellipse.\"
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\n" ); document.write( "Not a good example, imo.
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\n" ); document.write( "PS A lot of teachers don't have a good grasp of math.
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\n" ); document.write( "3(x^2-2x+1)+4(y^2-6y+1)=0-39+3+36
\n" ); document.write( "3(x-1)^2+4(y-3)^2=0\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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