Completing the square
We are given x2+bx. To complete the square means
to find the numbers that fill in the blanks correctly in
x2 + b x = (x + ___)2 - _____.
To do this, we first fill in the first blank with b/2, and then
we square that to fill in the second blank.
For example, to complete the square on x2 + 4/5 x,
x2 + 4/5 x = (x + 2/5)2 - ___
and then we square 2/5 for the other blank.
x2 + 4/5 x = (x + 2/5)2 - 4/25
The applet will present problems of this kind and let you fill in
the answer. If you get something wrong, it will try to figure
out what you did, and will give you the right answer.
You should verify that
x2 + b x = (x + b/2)2 - b2/4
is an identity.