Question 115425
You are off to a good start, but have some errors in your work


{{{x^2+(x+1)^2=85}}} You have the correct equation. So let's start there



{{{x^2+x^2+2x+1=85}}} Foil 



{{{x^2+x^2+2x+1-85=0}}} Subtract 85 from both sides



{{{2x^2+2x-84=0}}} Combine like terms



{{{2(x+7)(x-6)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x+7=0}}} or  {{{x-6=0}}} 


{{{x=-7}}} or  {{{x=6}}}    Now solve for x in each case



So our answer is 

 {{{x=-7}}} or  {{{x=6}}} 



So if {{{x=-7}}} , then the first number is -7. Now let's find the second number


{{{-7+1=-6}}}


So the second number is -6


So one pair of numbers is -7, -6


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Now if {{{x=6}}} , then the first number is 6. Now let's find the second number


{{{6+1=7}}}


So the second number is 7


So another pair of numbers is 6,7


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Answer:


This means the two numbers are either 6, 7 <b> OR </b> the two numbers -7,-6