The sum of the square of a positive number and the square of 44 more than the number is 8080. what is the number?

Let the number be x, therefore, its square is x², and 44 more than the number is x+44 whose square is (x+4)².
Thus the sum will be x² + (x+44)²² = 8080
                                  x² + x² + 88x + 1936= 8080 Combining the right terms 
                                  2x² + 8x - 6144 = 0 dividing by 2
                                     x² + 44x - 3072 =0 solving for x
                          x = 37.6 or -81.6
Therefore, the positive number is 37.6
                                

Let the unknown number be x
   x^2 + (x + 44)^2 = 8080
 x^2 +x^2 +88x +44^2 = 8080
 2x^2 +88x + 1936-8080=0
 2x^2 +88x - 6144 = 0
   divide through by 2
 x^2 + 44x -3072 =0
   Solving the quadratic equation, we have
 x= 37.65 or - 81.65

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