dimitri is solving the equation $x^{2}-10x = 21$. which value must be added to both sides of the equation to…

Explanation:

Step1: Recall perfect - square trinomial form

For a quadratic expression of the form $x^{2}+bx$, to make it a perfect - square trinomial $x^{2}+bx + c$, the value of $c=\left(\frac{b}{2}\right)^{2}$.

Step2: Identify the value of b

In the given equation $x^{2}-10x = 21$, the coefficient of $x$ is $b=- 10$.

Step3: Calculate the value of c

Substitute $b = - 10$ into the formula $c=\left(\frac{b}{2}\right)^{2}$. We have $\left(\frac{-10}{2}\right)^{2}=(-5)^{2}=25$.

Answer:

C. 25