Question 1005637
d = number of diagonals
n = number of sides


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In this case,
d = 779
n = unknown (we're solving for this)


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We will use the formula {{{d = (n(n-3))/2}}}
Plug in {{{d = 779}}} and solve for n


{{{d = (n(n-3))/2}}}


{{{779 = (n(n-3))/2}}}


{{{779*2 = 2*((n(n-3))/2)}}} Multiply both sides by 2


{{{1558 = n(n-3)}}}


{{{1558 = n^2-3n}}}


{{{1558-1558 = n^2-3n-1558}}} Subtract 1558 from both sides


{{{0 = n^2-3n-1558}}}


{{{n^2-3n-1558 = 0}}}


Use the quadratic formula to find that {{{n=41}}} or {{{n=-38}}}. 


Ignore {{{n=-38}}} since it doesn't make sense to have a negative number of diagonals.


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The only solution is {{{n=41}}}


There are 41 sides.