how do you complete the square of x^2-2x and y^2-2y?

Question

is it even possible?

Answer 1

You "complete the square" by adding what is missing to make a square... then subtracting it again.

If you add a and subtract a to an equation, you have not changed the equation's value, becasue you will have added (a - a) = 0. You can add zero as much as you want.

In the case of x^2 -2x, you are looking for a value that will create a square of the form (x-m)^2 = x^2 - 2x + a.
(the sign is minus because of the -2x).

The clue is usually that the middle coefficient (in this case 2) must be twice the product of m and the coefficient of x inside the bracket (in this case, that is 1).
so 2 times (m*1) = 2, gives us that m=1.

(x-1)^2 = x^2 -2x +1
so, our a is 1
We can add 1 (and subtract 1).

x^2 -2x
x^2 -2x + 1 - 1
(x-1)^2 -1

The second problem is the same (except it is using a letter y instead of x).

---

If this is homework for a course where you are just beginning to solve such problems, then it is sufficient, for this problem, to say that

you complete the square by adding 1
(and then show how adding 1 makes it a square)

Answer 2

You "complete the square" by adding what is missing to make a square... then subtracting it again.

If you add a and subtract a to an equation, you have not changed the equation's value, becasue you will have added (a - a) = 0. You can add zero as much as you want.

In the case of x^2 -2x, you are looking for a value that will create a square of the form (x-m)^2 = x^2 - 2x + a.
(the sign is minus because of the -2x).

The clue is usually that the middle coefficient (in this case 2) must be twice the product of m and the coefficient of x inside the bracket (in this case, that is 1).
so 2 times (m*1) = 2, gives us that m=1.

(x-1)^2 = x^2 -2x +1
so, our a is 1
We can add 1 (and subtract 1).

x^2 -2x
x^2 -2x + 1 - 1
(x-1)^2 -1

The second problem is the same (except it is using a letter y instead of x).

Answer 3

How about add 1.

x^2 -2x +1 = (x-1)^2

or

y^2 -2y +1 = (y-1)^2

I think this will work! Hope this helps.