
Richard C. answered 06/01/16
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Chayil,
After the appropriate number of weeks (x), the money saved by both will be the same. That means at that time the two functions will equal each other:
g(x) = f(x)
So:
x2 + 46 = 60 + 5x
Rearranging terms:
x2 - 5x - 14 = 0
This quadratic function has two factors:
(x - 7)(x + 2) = 0 (-7 * 2 = -14 and -7 + 2 = -5)
Then, either x - 7 = 0 or x - 2 = 0
x - 7 = 0 => x = 7
x + 2 = 0 => x = -2
x =7 weeks is correct since we can't have a negative number of weeks.
Hope this helps!

Richard C.
Chayil,
Any quadratic function (the largest power of x is 2 like the one in your problem) has two solutions. A quadratic, when graphed, looks like a parabola. Sometimes, the parabola crosses the x-axis at two places: two solutions for x.
In the case here, we needed to factor the quadratic to find what the two x's are. Any quadratic factored will look like:
(ax + c)(bx + c)
The two factors we found have this appearance. The reason we only used one of them is because we needed to find weeks and that can't be negative.
Make sense?
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06/01/16

Richard C.
meant (ax + c)(bx + d).
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06/01/16
Chayil H.
06/01/16