Question

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

Answer 1

-7/2

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,

Answer 2

9514 1404 393

Answer:

a = -3.5

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