.
So,
I am trying to understand where I am getting these types of questions wrong, it seems algebra is not my best subject at the moment.
x^2 - 8x - 5
(x - 4)^2 - 16 + 5 = (x - 4)^2 - 11
Check it;
(x - 4)^2 - 11 = x^2 - 8x + 5 + 11 = x^2 - 8x + 16
I think the problem is in the (x - 4) area as this does not work back out to the original question. I have also tried (x - 2)^2 but this also results in x^2 + 4x + 4, which is not the same.
My course book talks a lot about halfing the coefficients of x, but I am missing something somewhere?
So if I am reading your example correctly, you are saying that it is correct to carryout a subtraction from the LHS and Add - 11 to the RHS.
(x - 4)^2 - 11 - 11 = x^2 - 8x + 16 - 11 = x^2 - 8x - 5
I tried another method of algebra;
(x – 4)2 = – 11x2 – 8x – 5(x – 4)2 – 16 + 5
Check;
(x – 4)2– 11 = x2 – 8x - 5 – 11
= x2 – 8x - 16
(x – 4)2 – 11 = x2 – 8x - 16 + 11
= x2 – 8x – 5
The original equation was as you say; x^2 - 8x - 5. I understand the half term (x - 4)^2 but -4^2 = - 16 which is why I changed the sign convention from + 5 to - 5.
So in your example above because you are saying x^2 - 8x + 5, you are saying that (x - 4)^2 - 11 is correct, but I changed the - 5 to a + 5 from - 16 to get - 11.
when I add -11 to both sides I get x^2 - 8x - 5, which is the original equation, so are you saying that I am wrong?
Thanks
David
-16 is the right thing to put, but it looks like you got it for the wrong reason. When you expand (x-4)^2, you should do (-4)^2, which equals 16. But that has nothing to do with the 5.
What completing the square does is to represent algebraically what it would mean to literally fill in an incomplete square. You're on the right track with (x-4)^2, but this gives x^2-8x+16. But you can't just go adding 16 to one side of an equation, so you have to add it to the other side or subtract it again from the same side, which is why you're right by having -16 there.
This has nothing to do with the -5 though, and I'm not sure why you tried to change it.
You've to be careful with notations like that, it can be very confusing.
Start with:
Well, you want to have so you have to substract a term -21 from each side, because and this what you want, so:
Hi Siron, I have been on a learning curve with this, but now I understand the method used to find the square. We had different ideas regarding the value 16?
This is what I have learned;
x^2 - 8x - 5
(x - 4)^2 - 16 - 5
(x - 4)^2 - 21
(x - 4)^2 - 21 = x^2 - 8x + 16 - 21
= x^2 - 8x - 5
However all though all the above has been a learning curve, I did not find the solution in completed square form?
(x - 4)^2 - 16
David