Question

The sum of a number and its square is 72. Find the number.

Answer 1

Let the number be x
therefore
\[\huge x^2 +x = 72 \rightarrow x^2 +x -72=0\]
\[\huge \rightarrow x^2 +9x-8x -72=0\]
\[\huge \rightarrow x(x +9)-8(x +9)=0\]
\[\huge \rightarrow (x +9)(x-8)=0\]
\[\huge \rightarrow (x +9)=0 or (x-8)=0\]
\[\huge x=-9 or x=8\]
Hence the required numbers are -9 or 8

Answer 2

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