can someone exaplain completing the square please
- Thread starter yantorsen
- Start date
If you have a quadratic, (ax^2 + bx + c) x^2 + 8x + 12, and you want to solve it by completing the square, do this:
(x + 1/2 b)^2 + d.
The squared brackets will give you a^2 + b.
(x + 4)^2 in this case.
Then once you have multiplied out the brackets, you will have x^2 + 8x + 16. That isn't what you started with. It is 4 off the last number. So you now have to change it.
(x + 4)^2 - 4
Expanding those brackets will give you x^2 + 8x + 12. Right?
So now you have:
(x + 4)^2 - 4 = 0
Just solve as normal...
(x + 4)^2 = 4
(x + 4) = +/- 2
x + 4 = +/- 2
x = -2 or -6
Note: I changed the example quadratic to make it easier, so if you notice something is wrong, that is why.
(x + 1/2 b)^2 + d.
The squared brackets will give you a^2 + b.
(x + 4)^2 in this case.
Then once you have multiplied out the brackets, you will have x^2 + 8x + 16. That isn't what you started with. It is 4 off the last number. So you now have to change it.
(x + 4)^2 - 4
Expanding those brackets will give you x^2 + 8x + 12. Right?
So now you have:
(x + 4)^2 - 4 = 0
Just solve as normal...
(x + 4)^2 = 4
(x + 4) = +/- 2
x + 4 = +/- 2
x = -2 or -6
Note: I changed the example quadratic to make it easier, so if you notice something is wrong, that is why.
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didn't really get any of that tbh, i dnt know really know what a quadratic is.
how do you remember all that in an exam?
A quadratic equation is an equation where ax^2 + bx + c = 0. a, b and c are the coefficients for powers of x.
In the last example, a = 1, b = 8, and c = 12.
The first step is to divide b by 2, and put it in the standard brackets (x + number). Square this bracket.
When the bracket is expanded, it will give you an expression that isn't the original equation. You need to either add or subtract something to end up with the original equation. I called this number d in my last example.
Once you have worked out the brackets and what d is, solve as normal.
Carry d over to the right hand side, square root both sides, and then carry over the number that was in the bracket before over for the 2 values of x.
It's easy to remember in an exam. You know the steps, which are all logical and "make sense" (don't know how to explain it), they follow on from each other. Practice a few completing the square questions to help you remember how to do them.
Okay. Sure.
x^2 + 6x - 19 = 0
Edit: you'll need a calculator for this. Or you could leave it in surd form. Doesn't matter as long as you get to the right answer.
Last edited:
Caporegime
- Joined
- 1 Mar 2008
- Posts
- 26,303
If:
a = apple
and:
p = pastry
What is a+p?
Apple Pie.
a = apple
and:
p = pastry
What is a+p?
Apple Pie.
its C1 so its non-calculator, so here is what i got and im pretty sure its wrong:
x^2 + 6x -19 = 0
x (x+6) - 19 = 0
x (x+6) = 19
x = 19/x+6
Tut tut, still not doing your work I see
Anyway, isn't quadratics taught in the first year of GCSE?Didn't you think to ask your Maths teacher for help?
yeah it is, but it's in c1 as level as well, and I have asked my teacher, but I just can't get my head around it...
if i fail this test though i get taken off the course, it's a retake of Chapters 1 + 2 of C1, I got 3/24 the first time
In C1, you would be leaving your answer in surds form.
(x + 3)^2 - d = 0 would be the first step.
Multiplying this out...
x^2 + 6x + 9 - d = 0
Is the next step.
yeah it is, but it's in c1 as level as well, and I have asked my teacher, but I just can't get my head around it...
if i fail this test though i get taken off the course, it's a retake of Chapters 1 + 2 of C1, I got 3/24 the first time
Oh I see now, C1 paper is Edexcel AS Maths...still, quadratics is a segment of GCSE.
http://www.metacafe.com/watch/1253805/as_level_maths_revision_ocr_edexcel_core_c1/
Perhaps this revision video might help, my explanation would just be the same as Fraggr's and that doesn't seem much use to you.
Yep, Shimmy is right.
I have to go to bed now (school tomorrow). But the correct answer and workings are:
********************************************
********************************************
x^2 + 6x - 19 = 0
(x + 3)^2 = x^2 + 6x + 9
- 19 - 9 = -28
(x + 3)^2 - 28 = 0
(x + 3)^2 = 28
(x + 3) = +/- root 28
(x + 3) = +/- root (4 x 7)
(x + 3) = +/- 2 root 7
x = -3 +/- 2 root 7
*******************************************
*******************************************
Hope that helps. I did every step of it, although you don't need to go into that much detail in an exam with the rearranging.
I have to go to bed now (school tomorrow). But the correct answer and workings are:
********************************************
********************************************
x^2 + 6x - 19 = 0
(x + 3)^2 = x^2 + 6x + 9
- 19 - 9 = -28
(x + 3)^2 - 28 = 0
(x + 3)^2 = 28
(x + 3) = +/- root 28
(x + 3) = +/- root (4 x 7)
(x + 3) = +/- 2 root 7
x = -3 +/- 2 root 7
*******************************************
*******************************************
Hope that helps. I did every step of it, although you don't need to go into that much detail in an exam with the rearranging.
if you can't get your head around this after asking your teacher for help, you should probably think about putting in a LOT more effort or changing course to something you have a hope of passing. 3/24 seems low for anyone who even turned up to class.