Question

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

Answer 1

Explanation:

`x^(2) -7x+c=(x+a)^(2)`

`x^(2) -7x+c=x^(2) +2ax+a^(2)`

`-7x=2ax\\a=-7/2`

`a^(2) =c\\c=(-7/2)^(2) =49/4`