Question

To complete the square of $x^2+10x$, you would (add/subtract) the number ______.

Short answer

To complete the square of $x^2+10x$, you would add the number $\underline{25}$.

Step-by-step solution

Step 1. Given information

Polynomial is$x^2+10x$.

Step 2. Find the number to be added or subtracted.

For a perfect square trinomial in the form of $a{x}^2+bx+c$, we can solve for $c$using the formula $c={\left(\frac{b}{2}\right)}^2$

We have $a=1,b=10$

Therefore,

$\begin{array}{rcl}c& =& {\left(\frac{10}{2}\right)}^2\\ & =& 5^2\\ & =& 25\end{array}$

Thus, the perfect square trinomial is $x^2+10x+25$

Therefore, to complete the square of $x^2+10x$, you would add the number $25$.