What value should be added to the expression to create a perfect square? x^2 - 20x

show work, i don't just want handed the answer without explaination.

: )

To complete the square:
we take the coefficient ox "x" (which in this problem is -20)
we divide it by 2
square that number
then add it to both sides of the equation

-20 / 2 = -10
-10^2 = 100
then we add 100 to both sides of the equation:
x^2 -20x
x^2 -20x +100 = 100

To get the roots of the equation, we take the square root of both sides:
(x -10) * (x-10) = 10
(x-10) = square root (10)
x-10 = 3.1622776602
x1 = 13.1622776602
and don't forget that square root of 10 also equals  -3.1622776602
x2 = 10 - 3.1622776602
x2 =  6.8377223398

A’b’c’ are the coordinates to the new location of the transformed triangle abc. find the distance between the coordinates points to use for your calculations.