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:

x

^{2}+ 46 = 60 + 5xRearranging terms:

x

^{2}- 5x - 14 = 0This 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