Question 1014284
Find two consecutive odd integers such that their product is 35 more than 8 times their sum.
<pre>Let smaller integer be S
Then larger is: S + 2
We then get: S(S + 2) = 8(S + S + 2) + 35
{{{S^2 + 2S = 8(2S + 2) + 35}}}
{{{S^2 + 2S = 16S + 16 + 35}}}
{{{S^2 + 2S - 16S - 51 = 0}}}
{{{S^2  - 14S - 51 = 0}}}
(S - 17)(S + 3) = 0 ------- Factoring the above trinomial
Smaller integer, or S = 17          OR          S = - 3

If the smaller integer = {{{highlight(highlight_green(highlight(17)))}}}, then larger integer = 17 + 2, or {{{highlight(highlight_green(highlight(19)))}}}    
However, if the smaller integer = {{{highlight(highlight_green(highlight(- 3)))}}}, then larger integer = - 3 + 2, or {{{highlight(highlight_green(highlight(- 1)))}}}