Question

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

Answer 1

9514 1404 393

Answer:

  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

Answer 2

Answer:

-7/2

Step-by-step explanation:

Expanding (x + a)^2, we get  x^2 - 7x + c = x^2 + 2ax + a^2

Since this must hold for all x, the coefficients on both sides must match. Thus, -7 = 2a and c = a^2. From the first equation,