Answer
The number to add is $25$.
The factored form is $(x+5)^2$.
Work Step by Step
The given expression ieumbes $x^2+10x$.
This is in the form $x^2+bx$ where $b=10$.
To find the number to add to complete the square, use the formula $\left(\frac{1}{2}b\right)^2$ to obtain:
$\left(\frac{1}{2}b\right)^2=\left(\frac{1}{2}\cdot 10\right)^2=5^2=25$
Thus, the number to be added complete the square is $25$.
Add $25$ to the given expression.
$=x^2+10x+25$
$=x^2+2\cdot 5 \cdot x+5^2$
Use special formula $a^2+2ab+b^2=(a+b)^2$ where $a=x$ and $b=5$.
$=(x+5)^2$
Hence, the factored form is $(x+5)^2$.
