I think that presentation is confusing too!
Try expanding this \((x+7)^2\) and you will get \(x^2+17x+49 \)
Do it to make sure you know how and to check I did it right.
so I have \(x^2+14x+49=(x+7)^2\)
Notice if I half the 14 I get 7
If I square the 7 I git 49
so
\(x^2+14x+(\frac{14}{2})^2=(x+\frac{14}{2})^2\)
\(\)
If there is no number in front of the x^2 except for an invisible 1 then this will always be true.
Consider your example:
\(x^2 - 7x + c = (x + a)^2\)
c will be half of -7
a will be (half of -7) squared.
So you complete this bit for me please.