quadratic equation, completing the square

[mollykins]

yesterday in maths, we were going over, how to solve quadratic equations by completing the square, and the teacher put some equations to solve on the board.

He said that if we were confident and could easily do the rest, we could try the last one, which is the kind of thing you do at a-level.

However, i didn't have time to do it, but jotted down the question and the answer, but can't for the life of me work out how to get from one to the other, by completing the square.

so how do you turn ax² + bx + c = 0

into x = -b plus/minus the square root of b² - 4ac
............---------------------------------
-------------------------

....................................2a

????????? thaks for the help, i hope it turns out in the right format so you can udnerstand the equation.

[D_James]

Reaches for the JD....

[mollykins]

oops its come out wrong, i tried using full stops, to make the format right it should be the quadratic formula.

[D_James]

I apologise for my flippancy mollykins, the old brain matter is not in gear. Why not try looking for a Maths website?

[mollykins]

I've looked at a couple and unsuprisingly its all to complicated, its only as level maths, i jsut want someone to go through it step by step, its really annoying me now.

[sddsddean]

This is the simplest explanation I can find
http://www.analyzemat.../proof_quadratic.html

[mollykins]

thanks, all the other examples i found were way to complicated.

[Bloss]

if you have ax² + bx + c = 0
start by dividng by a x² + (b/a) x + c/a = 0
put into bracket as required from the completing the square method
(x + b/2a) ² - (b/2a)² + c/a = 0
square (b/2a) (x + b/2a) ² - b²/4a² + c/a = 0
rearrange (x + b/2a) ² = b²/4a² - c/a
change c/a to equivalent fraction 4ac/4a² to make a common denominator on rhs (x + b/2a) ² = b²/4a² - 4ac/4a²
simplify rhs (x + b/2a) ² = (b² - 4ac)/4a²
square root both sides x + b/2a = +/- (sq root (b² - 4ac) ) /2a
then move b/2a x = -b/2a +/- (sq root (b² - 4ac) ) /2a
all rhs has common denominator 2a, so can be made a single fraction
x = (-b +/- (sq root (b² - 4ac) ) )/2a
This is the method. Let me know if it makes any sense at all!! If there are one or two lines you don't understand I could clarify.
Hope it helps...

[rov1200]

Completing the Square.

If you look halfway down this Wickipedia article it tells you how to do this:

http://en.wikipedia.o...ki/Quadratic_equation

[bibblebub]

any older readers: didn't this used to be done at O-level (not A-level)?

[Prudie]

Yes. Sign of the times eh!

[kawakiri]

yep O level, quartic at a level

[bibblebub]

that make me feel despondent for various reasons

[factor-fiction]

Yes, at O level you had to be able to complete the square and use the quadratic formula to solve equations. You definitely still have to do the latter at GCSE (for Higher tier anyway) and I think you also have to complete the square.
Whay mollykins is doing is deriving the quadratic formula. I don't recall having to do that at O level

[Prudie]

Yes but she is deriving the quadratic formula by completing the square. I recall doing that at O level and it being the way the formula was first introduced when we moved on from those equations that could not be solved just by playing with the factors of a and c.
On a lighter note my daughter got an A at GCSE and she doesn't know her tables, counts on her fingers at times, doesn't get the hang of percentages.......

[factor-fiction]

Yes, one of my GCSE students couldn't work out how much change you get from a £5 note when buying something costing £4.79. She gave up after 5 minutes and numerous wrong answers. Most pupils don't know their tables beyond the 5 times table. Some of the stuff we did at O level such as calculus went years ago but the Higher paper still contains Trig, Pythagoras, quadratic equations, sine curves, surds etc

[mollykins]

We still have to some of it, that's why i could try and solve it, but the equation i tried to put in my question is the easiest of the a-level stuff.

[mollykins]

bloss i do understand it, thanks, i kind of knew how to do it, but i either kept going wrong somewhere or i did things in the wrong order.

We have to know our times tables up to 12 x12 and know the squared numbers up to 20 x 20 and cubed number up to 10 x 10 x 10 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[kawakiri]

Why up to 12x table.

[bibblebub]

yeah, they sounds very imperial???

[mollykins]

I dunno, i supose it makes stuff like finding the lowest common multiple and highest common denominator etc quicker and easier, on the non calculator paper.