AIDS Cases From 1993 to 2003 the cumulative number

N of AIDS cases in thousands can be approximated by N = -2x^2 + 76x + 430, Where x = 0 corresponds to the year 1993.

Year 1993 1995 1997 1999 2001 2003

Cases 422 565 677 762 844 930

(c) Rewrite the equation with the right side completely

factored.

Can someone explain to me how to do this please

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Rewrite the equation with the right side completely

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AIDS Cases From 1993 to 2003 math help?

You will see solution.

-2(x+5)(x-43)

To rewrite the equation N = -2x^2 + 76x + 430 with the right side completely factored, you need to factor the quadratic expression -2x^2 + 76x + 430.

Step 1: Start by finding the greatest common factor (GCF) of the coefficients. In this case, it is 2.
-2x^2 + 76x + 430 can be rewritten as 2(-x^2 + 38x + 215).

Step 2: Now, focus on factoring the quadratic expression within parentheses. You need to find two numbers whose product is equal to the product of the coefficient of x^2 term (-1) and the constant term (215), and whose sum is equal to the coefficient of the linear term (38). In this case, -1*215 = -215, and the only pair of numbers that meets the requirement is 5 and -43 (-5 * 43 = -215, -5 + (-43) = -48).

-2x^2 + 76x + 430 becomes 2(-x + 5)(x - 43).

So, the equation with the right side completely factored is:
N = 2(-x + 5)(x - 43).