document.write( "Question 7575: Can you please help me find two consecutive positive integers that the sum of their squares is 85. \n" ); document.write( "

Algebra.Com's Answer #4176 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
Consecutive integers: x, x+1. Sum of their squares equal 85: \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: x=6,x=-7.
Graphical form: Equation $\"x%5E2%2B%28x%2B1%29%5E2=85\"$ was fully solved.
Text form: x^2+(x+1)^2=85 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+x%5E2%2B%28x%2B1%29%5E2=85+%29\"$
For tutors: simplify_cartoon( x^2+(x+1)^2=85 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"x%5E2%2B%28x%2B1%29%5E2=highlight_red%28+85+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-85+%29\"$
It becomes $\"x%5E2%2B%28x%2B1%29%5E2-highlight_green%28+85+%29=0\"$ .
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Look at $\"highlight_red%28+x%5E2%2B%28x%2B1%29%5E2-85+%29=0\"$ .
Equation $\"highlight_red%28+x%5E2%2B%28x%2B1%29%5E2-85=0+%29\"$ is a quadratic equation: 2*x^2+2*x-84 =0, and has solutions 6,-7
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=6,x=-7.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "-7 is not positive, so the solution that we are allowed to have is x=6, the next integer is 7. 6,7 \n" ); document.write( "

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