Diagonals

What x-gon has 54 diagonals?

Correct result:

x =  12

Solution:

54=n(n−3)/2  −0.5n2+1.5n+54=0 0.5n2−1.5n−54=0  a=0.5;b=−1.5;c=−54 D=b2−4ac=1.52−4⋅0.5⋅(−54)=110.25 D>0  n1,2=−b±D2a=1.5±110.251 n1,2=1.5±10.5 n1=12 n2=−9   Factored form of the equation:  0.5(n−12)(n+9)=0  x>0  x=n1=12

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