You are looking for the moment when the two expressions are equal.
60 + 5x = x2 + 46
subtract 60+ 5x from both sides
0 = x2 -5x - 14
factor
0 = (x + 2)(x - 7)
which is true for x = -2 and x = 7,
but -2 weeks is not an acceptable answer,
leaving x = 7 weeks
Elwyn D.
tutor
Before you factor you can only guess at various values for x until one works. When you factor the equation you have two binomials that reveal the two roots. Those two roots are the only two numbers anywhere in the real numbers which will satisfy the equation. It just happens in this case that one of the solutions is meaningless because the concept of -2 weeks is obviously a non-sense cal answer.
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06/01/16
Elwyn D.
tutor
Nonsensical
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06/01/16
Chayil H.
06/01/16