Completing the square in Maths?

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kr3rdparty

kr3rdparty

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Im in 9th grade and i was getting a lot of questions where u had to complete the square when the Coefficient of x was greater than 1. Any help would be great within like a week or 2 because im having the regents in 2 weeks
 
I'm not sure what you mean by completing the square, I think you may be talking about this:
A quadratic function (function where X's exponent is 2) can be written like this:
AX^2 + BX + C, where A,B and C are the coefficients and (X^2) means X's exponent is 2.
Also, there exists something called the square of a binomial, which is (A+B)^2, and can also be expressed as A^2 + 2AB + B^2.
For example, if you have (X+2)^2, that's the same as writing X^2 + 4X + 4. This also means that you can make the reverse process: if you have X^2 + 4X +4 you can write it as (X+2)^2.
The thing is, what happens if your quadratic function isn't exactly the square of a binomial? Well, you start assuming you can make a square binomial with your quadratic function. For example, we have: 9x^2 + 6x + 3, if we compare this formula with the square of a binomial, we can observe a couple of things:
If it was a square of a binomial, A^2 would have to be = to 9X^2, if we simplify this, A=3X, so, we know the square would have this form: (3x+?),^2 as A contains an X with exponent 1, 2*A*B will have to contain an X with exponent 1. Which member of our quadratic formula has an X with exponent 1? that's right: 6X... this means: 6X = 2AB, since we knew that A=3X, 6X=2*3X*B, 6X=6XB, 1=B. There we are, our square is (3x+1)^2.... but, what happens if we calculate this square?, it gives: 9x^2 + 6x + 1, and our formula is 9x^2 + 6x + 3. Something's not right, but this is really easy to solve, if (3x+1)^2 = 9x^2+6x+1, and we need a formula that involves a square of a binomial but its C is = 3, then, we simply add 2 to the numbers we got... this means: (3x+1)^2 + 2 = 9x^2 + 6x + 1 +2 = 9x^2 + 6x + 3. So, (3x+1)^2 + 2 means the same as our quadratic function and has a square of a binomial.

Too Long, Didn't Read:
quadratic function = AX^2 + BX + C
square of binomial = (D+E)^2 = D^2 + 2DE + E^2
Don't care about the independent term by now, assume D^2 = AX^2 and BX=2DE. Get the values of D and E. Calculate the solution of the binomial (D^2+2DE+E^2), A and B will be the same as in your quadratic formula, if C differs, compensate that difference by adding or substracting the difference, the final result will look like: (D+E)^2 + F = AX^2 + BX + C
 
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Oh i get it now
For example, we have: 9x^2 + 6x + 3, if we compare this formula with the square of a binomial, we can observe a couple of things:
If it was a square of a binomial, A^2 would have to be = to 9X^2, if we simplify this, A=3X, so, we know the square would have this form: (3x+?),^2 as A contains an X with exponent 1, 2*A*B will have to contain an X with exponent 1. Which member of our quadratic formula has an X with exponent 1? that's right: 6X... this means: 6X = 2AB, since we knew that A=3X, 6X=2*3X*B, 6X=6XB, 1=B. There we are, our square is (3x+1)^2.... but, what happens if we calculate this square?, it gives: 9x^2 + 6x + 1, and our formula is 9x^2 + 6x + 3. Something's not right, but this is really easy to solve, if (3x+1)^2 = 9x^2+6x+1, and we need a formula that involves a square of a binomial but its C is = 3, then, we simply add 2 to the numbers we got... this means: (3x+1)^2 + 2 = 9x^2 + 6x + 1 +2 = 9x^2 + 6x + 3. So, (3x+1)^2 + 2 means the same as our quadratic function and has a square of a binomial.
(D+E)^2 + F = AX^2 + BX + C
Click to expand...
That example was all i needed.
I was wondering what to put as the d in ur final equation when a was greater than one.
Thanks very much @J9794
 
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Im in 9th grade and i was getting a lot of questions where u had to complete the square when the Coefficient of x was greater than 1. Any help would be great within like a week or 2 because im having the regents in 2 weeks
Click to expand...
I usually do quadratic formula but if they make you complete the square do the the same steps and try and solve around it.
 
I used to have to complete the square all the time in trig via the quadratic function/formula. J9's explanation is really well put together.
 
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Me i dont know how to solve quadratic equation with the method of completing the square but there are other easier methods to use in solving a quadratic the equation . There is the fumbular method and factorisation method .For me the easiest is the fumbular method .In an exam the may or may not ask you to choose any any one .Me i always choose the Fumbular method
 
Honestly I wouldn't be able to explain this. I'm currently taking college Algebra which I'm actually repeating since I failed it back in spring. I'm still really horrible at remembering some of the things I've been learning and my final is Tuesday LOL I'm gonna die.
 
Completing the square isn't incredibly difficult and there are many YouTube vids that are easy to find and can help. I suppose it is a bit tricky, but with a few practice runs you'd probably be able to handle it in any situation.
 
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