Richard C. answered • 06/01/16

Yes, You Can Learn Math!

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