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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
Please help, as I do not understand fully how to do this.
(a)Quote:
Originally Posted by greatersanta616
$\displaystyle (x+p)^2=(x+p)(x+p)=x(x+p)+p(x+p)=x^2+2xp+p^2$
Therefore, in $\displaystyle x^2+4x=1$ the "2p" term is 4, so p is 2.
But...$\displaystyle (x+2)^2=x^2+4x+4$
Hence
$\displaystyle x^2+4x=1\Rightarrow\ x^2+4x+4=1+4$
$\displaystyle (x+2)^2=5$
$\displaystyle x+2=\pm\sqrt{5}$
$\displaystyle x=-2\pm\sqrt{5}$
Try (d)
(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!Quote:
Originally Posted by greatersanta616
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.Quote:
Originally Posted by Archie Meade
