Question 680895
The 2 consecutive numbers are x and x+1
So the question in words is the same as below equation:
{{{(x^2)+(x+1)^2=85}}}

{{{x^2+x^2+2x+1=85}}}
Add and simplify
{{{2x(x+1)+1=85}}}
Subtract 1 from both sides
{{{2x(x+1)=84}}}
Divide by 2
{{{x(x+1)=42}}}
Distribute
{{{x^2+x=42}}}
Subtract 42
{{{x^2+x-42=0}}}
Find 2 numbers that add together that get 1 and multiply to get -42
They are 7 and -6
{{{(x+7)(x-6)=0}}}
X= -7 , 6
So 2 possible answers
(-7 and -6) or (6 and 7)
Check
{{{6^2+7^2=85}}}
{{{36+49=85}}}
{{{85=85}}}