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Solving an equation by "Completing the Square" where "a" coefficient isn't 1 ?

How would you go about solving this question, once I know how to do it. I will understand it fully but the book I am reading explains it in a really bad way with gaps and no references to how these "gaps" are meant to be filled.

3x2 - 12x - 7 = 0


The answer is : x = +/- sqrt(57)/3 + 2
Reply 1
Avatar for a9493r
a9493r
20
there is a specific formula used when the x cannot be resolved in the normal way ...and that answer comes by working out the formula...
Original post by ero
How would you go about solving this question, once I know how to do it. I will understand it fully but the book I am reading explains it in a really bad way with gaps and no references to how these "gaps" are meant to be filled.

3x2 - 12x - 7 = 0


The answer is : x = +/- sqrt(57)/3 + 2


You have to firstly divide by three to make the a coefficient equal to 1. So you get 3(x2-4x)-7=0. Note that I've only factorised out 3 from part of the function, that prevents us from having to deal with ugly fractions early on.
Reply 3
Avatar for a9493r
a9493r
20
http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/quadequationshirev3.shtml

this should give you an idea about the formula used...unfortunately I am not allowed to solve it for you here but I can say that you should compare the given equation to the normal eqt ax^2+bx+c and assign a,b,c values and then solve the formula...hope that helped :smile:
Reply 4
Avatar for ero
ero
OP
Thanks all, I should be able to find it out =]
Original post by ero
How would you go about solving this question, once I know how to do it. I will understand it fully but the book I am reading explains it in a really bad way with gaps and no references to how these "gaps" are meant to be filled.

3x2 - 12x - 7 = 0


The answer is : x = +/- sqrt(57)/3 + 2



I will try and solve this for you but obviously I am not allowed to give you the answers...anyway you times the 3 by 7 which=-21 and then think so what times to make 21 and adds or take away to make -12.....and you follow on from there.
Edit: this may require a quadratic formula....let me check if that would be so.
(edited 9 years ago)
Original post by ero
How would you go about solving this question, once I know how to do it. I will understand it fully but the book I am reading explains it in a really bad way with gaps and no references to how these "gaps" are meant to be filled.

3x2 - 12x - 7 = 0


The answer is : x = +/- sqrt(57)/3 + 2


Unfortunately my way(timesing the coefficient with the last number which was -7) does not work so you would have to use the quadratic formula which is a little bit complicating but not if you are used to it

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