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tuanle007
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x^2 + y^2 - 2pxy = (x-py)^2 - (py)^2 + y^2
can someone please help me with this. i totally forgot how to do completing the square.
can someone please help me with this. i totally forgot how to do completing the square.
tuanle007 said:x^2 + y^2 - 2pxy = (x-py)^2 - (py)^2 + y^2
can someone please help me with this. i totally forgot how to do completing the square.
tuanle007 said:ok, i understand the completing the square part,
but can someone explain how the next step is..
where does the (1-p)^2 comes about and things like that
thanks
tuanle007 said:i think i kinda remember it now..
what i did was I put everything on the left side as X and everything on the right as Y
so i have
x^2 - 2pxy = -y^2
then I complete the X on the left side
(x^2 - 2pxy) + (2py/2)^2 = -y^2 + (2py/2)^2
the left side factored out to be
(x-py)^2 = -y^2 + py^2
so then move everything to the left we get
(x-py)^2 + y^2 - py^2
That's the easy part! Long before you learned to "complete the square" you learned that "ax+ ay= a(x+ y)", the "distributive law" in technical terms. There is a y^2 term in both y^2 and -py^2 so : y^2- py^2= y^2(1)- y^2(p)= y^2(1- p).tuanle007 said:ok, i understand the completing the square part,
but can someone explain how the next step is..
where does the (1-p)^2 comes about and things like that
thanks
"Completing the square" is a mathematical technique used to solve quadratic equations. It involves manipulating the equation in order to create a perfect square trinomial, which can then be easily solved by taking the square root of both sides.
"Completing the square" is useful because it provides a systematic way to solve quadratic equations, which are commonly used in many areas of science and mathematics. It also allows us to find the vertex of a parabola, which has many practical applications.
The steps for completing the square are as follows:
"Completing the square" should be used when solving quadratic equations that cannot be easily factored or when finding the vertex of a parabola. It is also used in some geometric and optimization problems.
Some common mistakes to avoid when completing the square include forgetting to divide the coefficient of the x² term by 2, making mistakes when squaring the result, and forgetting to add the squared result to both sides of the equation. It is important to carefully follow each step to avoid errors.