Question

enter the correct value so that each expression is a perfect - square trinomial.
$x^{2}-10x + \boxed{25}$
complete
$x^{2}+\boxed{}x + 36$
done

Explanation:

Step1: Recall perfect-square formula

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

Step2: Match given terms to formula

We have $x^2 + \square x + 36$, so $a^2=36$. Solve for $a$:
$a = \pm\sqrt{36} = \pm6$

Step3: Calculate the middle term coefficient

The middle term is $2ax$, so $2a = 2\times(\pm6) = \pm12$

Answer:

$\pm12$