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While finding the amount of seed needed to plant his three square wheat fields,
\n" ); document.write( " Hank observed that the side of one field was 1 kilometer longer than the side
\n" ); document.write( " of the smallest field and that the side of the largest field was 3 kilometers
\n" ); document.write( " longer than the side of the smallest field. If the total area of the three
\n" ); document.write( " fields is 38 square kilometers, then what is the area of each field?
\n" ); document.write( ":
\n" ); document.write( "let x = side of the smallest field
\n" ); document.write( "then
\n" ); document.write( "(x+1) = side of the middle sized field
\n" ); document.write( "and
\n" ); document.write( "(x+3) = side of the largest field
\n" ); document.write( ":
\n" ); document.write( "x^2 + (x+1)^2 + (x+3)^2 = 38
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
\n" ); document.write( "Combine like terms
\n" ); document.write( "x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 = 38
\n" ); document.write( ":
\n" ); document.write( "3x^2 + 8x + 10 - 38 = 0
\n" ); document.write( ":
\n" ); document.write( "3x^2 + 8x - 28 = 0
\n" ); document.write( "Factor this to
\n" ); document.write( "(3x + 14)(x - 2) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "x = 2 km, 2^2 = 4 sq/km, area of the smallest field
\n" ); document.write( "and
\n" ); document.write( "2 + 1 = 3 km; 3^2 = 9 sq/km; the middle field
\n" ); document.write( "and
\n" ); document.write( "2 + 3 = 5 km; 5^2 = 25 sq/km; the largest field
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution:
\n" ); document.write( "4 + 9 + 25 = 38 \n" ); document.write( "