Question

complete the expression so it forms a perfect - square trinomial.
$x^{2}-5x +$
complete
$x^{2}+$ $x + 49$
done

Explanation:

Step1: Recall perfect square form

A perfect-square trinomial follows $x^2 + 2ax + a^2=(x+a)^2$.

Step2: Identify $a$ from constant term

Given constant term $49=a^2$, solve for $a$:
$a=\sqrt{49}=7$ or $a=-\sqrt{49}=-7$

Step3: Calculate the middle coefficient

Middle term coefficient is $2a$.
For $a=7$: $2a=2\times7=14$
For $a=-7$: $2a=2\times(-7)=-14$

Answer:

$\pm14$