Completing the square Watch

thefatone
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what does completing the square actually tell you?

i know can be used to
find the minimum point of a quadratic
to derive the quadratic formula
do c1 questions which require this skill

what uses does it have?
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B_9710
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Can be used to solve quadratics more conveniently.
Manipulate expressions in integrands to make things easier to integrate.
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john_jomcy98
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(Original post by thefatone)
what does completing the square actually tell you?

i know can be used to
find the minimum point of a quadratic
to derive the quadratic formula
do c1 questions which require this skill

what uses does it have?
Pretty much what you said. It's sort of an easier way to factorise a quadratic.
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thefatone
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(Original post by john_jomcy98)
Pretty much what you said. It's sort of an easier way to factorise a quadratic.
i know but it doesn't give the fully factorised version/using the forumla
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Student403
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It's used in FP3 to turn things in to a different form that is easier to integrate
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Zacken
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(Original post by thefatone)
Completing the square
I know that this isn't the directly related to the question but you might enjoy reading this post.
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Youngmetro
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(Original post by Zacken)
I know that this isn't the directly related to the question but you might enjoy reading this post.
can you have quadratics with imaginary numbers?
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thefatone
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(Original post by Student403)
It's used in FP3 to turn things in to a different form that is easier to integrate
(Original post by B_9710)
Can be used to solve quadratics more conveniently.
Manipulate expressions in integrands to make things easier to integrate.

that's new.... da how i wish i did further maths now >.>

(Original post by Zacken)
I know that this isn't the directly related to the question but you might enjoy reading this post.
will do...
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Zacken
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(Original post by Youngmetro)
can you have quadratics with imaginary numbers?
Yes. Do you mean as coefficients or factoring them over the complex plane? If it's the former: definitely, if it's the latter: still definitely. The complex number field acts as the algebraic extension or closure of the real number field, so you can definitely factorise a quadratic with real coefficients into two linear factors.
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atsruser
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(Original post by thefatone)
what does completing the square actually tell you?

i know can be used to
find the minimum point of a quadratic
to derive the quadratic formula
do c1 questions which require this skill

what uses does it have?
You have asked two different questions here, but I'll give an answer to the first: completing the square tells you that, given a rectangle, you can always find a square with a smaller square removed, with the same area as the rectangle. For example:

x^2+6x = x(x+6) is the area of a rectangle of sides x, x+6. But by competing the square, we have x(x+6) = (x+3)^2-3^2 which is the area of a square of side x+3 with a smaller square, area 3^2 removed.

You can see a graphical representation of this here: http://www.thestudentroom.co.uk/show...79&postcount=5
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Zacken
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(Original post by atsruser)
You can see a graphical representation of this here:
Perhaps more complicated than needs be, but meh:

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atsruser
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(Original post by Zacken)
Perhaps more complicated than needs be, but meh:

That's neat, but not very easy to follow, I think.
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Zacken
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(Original post by atsruser)
That's neat, but not very easy to follow, I think.
Yeah, I agree - I much preferred your simpler and more concise example.
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thefatone
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(Original post by atsruser)
You have asked two different questions here, but I'll give an answer to the first: completing the square tells you that, given a rectangle, you can always find a square with a smaller square removed, with the same area as the rectangle. For example:

x^2+6x = x(x+6) is the area of a rectangle of sides x, x+6. But by competing the square, we have x(x+6) = (x+3)^2-3^2 which is the area of a square of side x+3 with a smaller square, area 3^2 removed.

You can see a graphical representation of this here: http://www.thestudentroom.co.uk/show...79&postcount=5
(Original post by Zacken)
Perhaps more complicated than needs be, but meh:

thanks both of you, now i can understand why it's called completing the square xD
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