document.write( "Question 214195: the product of two consec. pos. intergers is 29 more than thier sum. find the intergers. \n" ); document.write( "

Algebra.Com's Answer #161791 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
The product of two consecutive positive integers is 29 more than their sum. find the integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be one positive integer and n+1 is the next consecutive positive
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\n" ); document.write( "\n" ); document.write( "Step 2. n(n+1) be the product between these positive integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. n+n+1=2n+1 be the sum of the two positive integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Then using Steps 2, 3 and the problem statement yields, n*(n+1)=2n+1+29 \r
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\n" ); document.write( "\n" ); document.write( "Step 5. The following steps will solve the equation in Step 4.\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: n=6,n=-5.
Graphical form: Equation $\"n%2A%28n%2B1%29=2n%2B1%2B29\"$ was fully solved.
Text form: n*(n+1)=2n+1+29 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+n%2A%28n%2B1%29=2n%2B1%2B29+%29\"$
For tutors: simplify_cartoon( n*(n+1)=2n+1+29 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"n%2A%28n%2B1%29=2%2An%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+29+%29\"$ .
Added fractions or integers together
It becomes $\"n%2A%28n%2B1%29=2%2An%2Bhighlight_green%28+30+%29\"$ .
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Look at $\"n%2A%28n%2B1%29=highlight_red%28+2%2An%2B30+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-2%2An+%29\"$ , $\"highlight_green%28+-30+%29\"$
It becomes $\"n%2A%28n%2B1%29-highlight_green%28+2%2An+%29-highlight_green%28+30+%29=0\"$ .
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Look at $\"highlight_red%28+n%2A%28n%2B1%29+%29-2%2An-30=0\"$ .
Expanded term $\"n\"$ by using associative property on $\"%28n%2B1%29\"$
It becomes $\"highlight_green%28+n%2An+%29%2Bhighlight_green%28+n%2A1+%29-2%2An-30=0\"$ .
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Look at $\"n%2An%2Bn%2Ahighlight_red%28+1+%29-2%2An-30=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"n%2An%2Bn-2%2An-30=0\"$ .
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Look at $\"highlight_red%28+n+%29%2Ahighlight_red%28+n+%29%2Bn-2%2An-30=0\"$ .
Reduce similar several occurrences of $\"highlight_red%28+n+%29\"$ to $\"highlight_green%28+n%5E2+%29\"$
It becomes $\"highlight_green%28+n%5E2+%29%2Bn-2%2An-30=0\"$ .
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Look at $\"n%5E2%2Bhighlight_red%28+n+%29-highlight_red%28+2%2An+%29-30=0\"$ .
Eliminated similar terms $\"highlight_red%28+n+%29\"$ , $\"highlight_red%28+-2%2An+%29\"$ replacing them with $\"highlight_green%28+%281-2%29%2An+%29\"$
It becomes $\"n%5E2%2Bhighlight_green%28+%281-2%29%2An+%29-30=0\"$ .
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Look at $\"n%5E2%2B%28highlight_red%28+1+%29-highlight_red%28+2+%29%29%2An-30=0\"$ .
Added fractions or integers together
It becomes $\"n%5E2%2B%28highlight_green%28+-1+%29%29%2An-30=0\"$ .
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Look at $\"n%5E2%2B%28highlight_red%28+-1+%29%29%2An-30=0\"$ .
Removed extra sign in front of $\"-1\"$
It becomes $\"n%5E2%2B%28-highlight_green%28+1+%29%29%2An-30=0\"$ .
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Look at $\"n%5E2%2Bhighlight_red%28+%28-highlight_red%28+1+%29%29%2An+%29-30=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$
It becomes $\"n%5E2-highlight_green%28+1+%29%2An-30=0\"$ .
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Look at $\"n%5E2-highlight_red%28+1+%29%2An-30=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"n%5E2-n-30=0\"$ .
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Look at $\"highlight_red%28+n%5E2-n-30+%29=0\"$ .
Equation $\"highlight_red%28+n%5E2-n-30=0+%29\"$ is a quadratic equation: n^2-n-30 =0, and has solutions 6,-5
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=6,n=-5.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "Step 6. Select the positive solution and in this case it's n=6.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. So the integers are 6 and 7. Note: The product is 42 which is 29 more than their sum of 13.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful. \r
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\n" ); document.write( "\n" ); document.write( "For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
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\n" ); document.write( "\n" ); document.write( "And good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J
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