document.write( "Question 716248: I have a word problem. \r
\n" ); document.write( "\n" ); document.write( "\"A picture has a square frame that is 2 inches wide. The area of the picture is one-third of the total area of the picture and frame. What are the dimensions of the picture to the nearest quarter of an inch?\"\r
\n" ); document.write( "\n" ); document.write( "I know that it is a quadratic equation and my teacher said that I have to solve it by completing the square. \n" ); document.write( "
Algebra.Com's Answer #439784 by lwsshak3(11628)\"\" \"About 
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A picture has a square frame that is 2 inches wide. The area of the picture is one-third of the total area of the picture and frame. What are the dimensions of the picture to the nearest quarter of an inch?\"
\n" ); document.write( "**
\n" ); document.write( "let x=length of side of square picture
\n" ); document.write( "x^2=area of picture
\n" ); document.write( "(x+4)=length of side of square frame
\n" ); document.write( "(x+4)^2=total area of picture and frame
\n" ); document.write( "..
\n" ); document.write( "x^2=1/3(x+4)^2=(x^2+8x+16)/3
\n" ); document.write( "3x^2=x^2+8x+16
\n" ); document.write( "2x^2-8x-16=0
\n" ); document.write( "x^2-4x-8=0
\n" ); document.write( "solve for x by completing the square:
\n" ); document.write( "(x^2-4x+4)-4-8=0
\n" ); document.write( "(x-2)^2=12
\n" ); document.write( "take sqrt of both sides
\n" ); document.write( "x-2=±√12
\n" ); document.write( "x=2±√12
\n" ); document.write( "x=2±3.46
\n" ); document.write( "x≈-1.46 (reject, x>0)
\n" ); document.write( "or
\n" ); document.write( "x≈5.5
\n" ); document.write( "dimensions of the picture: 5.5 by 5.5 inches\r
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