document.write( "Question 413304: can you help me find three consecutive integers such that the square of twice the first is 30 more than three times the product of the second and third? \n" ); document.write( "
Algebra.Com's Answer #290230 by ankor@dixie-net.com(22740)\"\" \"About 
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find three consecutive integers such that the square of twice the first is
\n" ); document.write( " 30 more than three times the product of the second and third?
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\n" ); document.write( "Three consecutive integers, x, (x+1). (x+2)
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\n" ); document.write( "(2x)^2 = 3(x+1)*(x+2) + 30
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\n" ); document.write( "square 2x and FOIL
\n" ); document.write( "4x^2 = 3(x^2 + 3x + 2) + 30\r
\n" ); document.write( "\n" ); document.write( "4x^2 = 3x^2 + 9x + 6 + 30
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\n" ); document.write( "Combine like terms on the left
\n" ); document.write( "4x^2 - 3x^2 - 9x - 36 = 0
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\n" ); document.write( "x^2 - 9x - 36 = 9
\n" ); document.write( "Factors to
\n" ); document.write( "(x - 12)(x + 3) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 12
\n" ); document.write( "and
\n" ); document.write( "x = -3
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\n" ); document.write( "12, 13, 14 are our 3 integers
\n" ); document.write( "or
\n" ); document.write( "-3, -2, -1, could also be the 3 integers
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\n" ); document.write( "Check both in the statement
\n" ); document.write( "(2*12)^2 = 3(13*14) + 30
\n" ); document.write( "576 = 546 + 30; confirms our solution of x=12
\n" ); document.write( "and
\n" ); document.write( "(2*-3)^2 = 3(-2 * -1) + 30
\n" ); document.write( "36 = 6 + 30; confirms the x = -3 solution
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