<PRE><B>Question 41579</B>
&lt;pre&gt;Given soccer fields are rectangular:
2 variables, the width, and the length of the soccer field.
&lt;font color=green&gt;The width is 5 longer than the length.&lt;/font&gt;
&lt;font color=red&gt;The width times the length is 336.&lt;/font&gt;
&lt;font color=orange&gt;The unit is yards.&lt;/font&gt;
&lt;font color=green&gt;W=L+5&lt;/font&gt;
&lt;font color=red&gt;WL=336&lt;/font&gt;
substitute for W in &quot;&lt;font color=red&gt;WL=336&lt;/font&gt;&quot;.
(L+5)L=336  distribute
L&lt;sup&gt;2&lt;/sup&gt;+5L=336  subtract 336 from both sides
L&lt;sup&gt;2&lt;/sup&gt;+5L-336=0  Factor (or use quadradic formula)

2 numbers which multiply to -336 and add to 5, so 1 number must be negative.
336=112*3=56*6=28*12=14*24=7*48, but you&#39;ll notice none of those have a difference of 5..let&#39;s try 2&#39;s
336=168*2=84*4=42*8=21*16 aha!  difference of 5. so we alter the equation:

L&lt;sup&gt;2&lt;/sup&gt;+5L-336=L&lt;sup&gt;2&lt;/sup&gt;-16L+21L-336 
Now we factor:
L&lt;sup&gt;2&lt;/sup&gt;-16L+21L-336  take out like terms:
L(L-16)+21(L-16)  put like terms 2gether
(L+21)(L-16)=0  so 1 of thoz = 0
L=-21, or it equals 16. A side is hardly negative; but definitely not for a football field, therefore L=16.
&lt;font color=green&gt;W=L+5&lt;/font&gt; so &lt;font color=green&gt;W=16+5&lt;/font&gt;, or 21.
W=21&lt;font color=orange&gt;yards&lt;/font&gt;
L=15&lt;font color=orange&gt;yards&lt;/font&gt;

..I&#39;m beginning to think there was a simpler way of figuring this out, I cannot put my finger on it.</PRE>