If \[x^2 - 7x + c = (x + a)^2\]for some constants $a$ and $c,$ then find $a.$

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  a = -3.5

Step-by-step explanation:

The square expands to ...

 (x +a)^2 = x^2 +2ax +a^2

That is, ...

  2ax = -7x . . . . . . match x-terms

  a = (-7x)/(2x) = -7/2

  a = -3.5

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)