1. ## Completing the square.

A level Mathematics. Use the method of completing the square to solve these quadratic equations. Give your answer in the form a(+or-)b root "n" where a and b are rational, and n is an integer.
a. x^2+4x-1=0
d. x^2-8x-3=0

2. Originally Posted by greatersanta616
A level Mathematics. Use the method of completing the square to solve these quadratic equations. Give your answer in the form a(+or-)b root "n" where a and b are rational, and n is an integer.
a. x^2+4x-1=0
d. x^2-8x-3=0

(a)

$(x+p)^2=(x+p)(x+p)=x(x+p)+p(x+p)=x^2+2xp+p^2$

Therefore, in $x^2+4x=1$ the "2p" term is 4, so p is 2.

But... $(x+2)^2=x^2+4x+4$

Hence

$x^2+4x=1\Rightarrow\ x^2+4x+4=1+4$

$(x+2)^2=5$

$x+2=\pm\sqrt{5}$

$x=-2\pm\sqrt{5}$

Try (d)

3. (d) x^2-8x-3=0
So..
(x-4)^2-19=0
Therefore.
(x-4)^2=19
henceforth...
x-4=(+or-)root 19
and...
x=4(+or-)root 19

Is this ok?

4. Originally Posted by greatersanta616
(d) x^2-8x-3=0
So..
(x-4)^2-19=0
Therefore.
(x-4)^2=19
henceforth...
x-4=(+or-)root 19
and...
x=4(+or-)root 19

Is this ok?
Yes, that's the completing the square technique..you got it fast!

I think that "a" and "b" being rational, would apply more to the case of using the quadratic formula,
however, those values, while being integers, are rational anyway.

5. Originally Posted by Archie Meade
Yes, that's the completing the square technique..you got it fast!

I think that "a" and "b" being rational, would apply more to the case of using the quadratic formula,
however, those values, while being integers, are rational anyway.
Thank you very much for this. It really helped.