document.write( "Question 249021: The product of two consecutive negative integers is 89 more than the their sum. Find the larger interger. \n" ); document.write( "

Algebra.Com's Answer #181488 by College Student(505) $\"\"$ $\"About$

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Let x = negative number
\n" ); document.write( "Let x-1 = consecutive negative number\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-1%29=89%2Bx%2Bx-1\"$
\n" ); document.write( " $\"x%5E2-x=88%2B2x\"$
\n" ); document.write( " $\"x%5E2-x-2x-88=0\"$
\n" ); document.write( " $\"x%5E2-3x-88=0\"$
\n" ); document.write( " $\"%28x-11%29%28x%2B8%29=0\"$
\n" ); document.write( "Possible solutions: x=11 and x=-8\r
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\n" ); document.write( "\n" ); document.write( "Let's see which answer fits our original problem:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-1%29=89%2Bx%2Bx-1\"$
\n" ); document.write( " $\"11%2811-1%29=89%2B11%2B11-1\"$
\n" ); document.write( " $\"11%2810%29=110\"$
\n" ); document.write( " $\"110=110\"$ <--- answer checks when x=110 and x-1=109.
\n" ); document.write( "However, even though it checks, it does not apply to our problem
\n" ); document.write( "because we are looking for negative consecutive numbers.\r
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\n" ); document.write( "\n" ); document.write( "Let's try the other one:
\n" ); document.write( " $\"x%28x-1%29=89%2Bx%2Bx-1\"$
\n" ); document.write( " $\"-8%28-8-1%29=89%2B%28-8%29%2B%28-8%29-1\"$
\n" ); document.write( " $\"-8%28-9%29=72\"$
\n" ); document.write( " $\"72=72\"$ <--- this answer checks and the solution set contains negative numbers!!
\n" ); document.write( "Solution set: x= -8, -9\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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