document.write( "Question 447847: Find two consecutive positive integers such that the sum of their squares is 41. \n" ); document.write( "
Algebra.Com's Answer #308255 by algebrahouse.com(1659)\"\" \"About 
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\"Find two consecutive positive integers such that the sum of their squares is 41.\"\r
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\n" ); document.write( "\n" ); document.write( "x = 1st positive integer
\n" ); document.write( "x + 1 = 2nd positive integer\r
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\n" ); document.write( "\n" ); document.write( "x² + (x + 1)² = 41 {sum of squares is 41}
\n" ); document.write( "x² + (x + 1)(x + 1) = 41 {when you square a binomial, multiply it by itself}
\n" ); document.write( "x² + x² + 2x + 1 = 41 {used foil method}
\n" ); document.write( "2x² + 2x + 1 = 41 {combined like terms}
\n" ); document.write( "2x² + 2x - 40 = 0 {subtracted 41 from both sides}
\n" ); document.write( "2(x² + x - 20) = 0 {factored 2 out}
\n" ); document.write( "2(x + 5)(x - 4) = 0 {factored into two binomials}
\n" ); document.write( "x + 5 = 0 or x - 4 = 0 {set each factor equal to 0, excluding the 2}
\n" ); document.write( "x = -5 or x = 4 {solved each equation for x}
\n" ); document.write( "x = 4 {only positive integer}
\n" ); document.write( "x + 1 = 5 {substituted 4, in for x, into x + 1}\r
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\n" ); document.write( "\n" ); document.write( "4 and 5 are the consecutive positive integers
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