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"?

Every weekday, mr. jones bikes from his home to his job. sometimes he rides along two roads, the long route that is shown by the solid lines. other times, he takes the shortcut shown by the dashed line. how many fewer kilometers does mr. jones bike when he takes the shortcut instead of the long route?

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Which are the possible side lengths of a triangle?