If using the method of completing the square to solve the quadratic equation x^2-19x+23=0 which number would have to be added to "complete the
square"?

The larger square has diagonal length 8. The diagonals of a square are congruent. The area of a square can be found by taking one-half the product of its diagonals. The area of the larger square is (1/2) 8*8 = 32. --- The area of the smaller square can be found in a likewise manner: Area = (1/2) 4*4 = 8 Area of shaded region = 32 - 8 = 24.0