The first thing you want to do is, you look at the "x" terms
basically that are in there and you want the coefficient
you want the coefficient of the "X" squared term to equal one
which it does in this case
if not , you have to factor it out.and i'll do something like that
in a separate example
so we have this condition. What we then do is
stick in a set of parenthases with the first two, give yourself a little space
and then i'm going to write my plus eight, give myself a little space, equals zero
so the whole point of how you complete the square is, you look at
whatever number is front of the "X" term, so in this case, the number in front of the "X"
the coefficient, on the "X " term is one-half (1/2, .5). we then take one half of that number.we always take one half of it
so one half of negative six, is negative 3.
and then what you do is,
you square it, and put that number back inside of there. so if we square it
we get positive nine.
okay, so we've actually thrown in a brand new number that wasn't there
before, we put in this positive nine.
that wasn't there
the way we can get rid of it, in this case,
is, I mean , basically,
you're just getting rid of the parenthasese
we would get back the original thing
except our plus nine would be there
well to cancel it out,we are going to subtract nine. okay,
notice this is all happening on the left side of the equals sign
okay so now, we just simplify down a little bit more
and the point is, you can write the stuff in parenthases as a perfect square
it actually factors down as "x" minus three , times "x" minus three
okay, and again, if you take whatever one half of the coefficient
on the "X" term was,
it was a negative three, that will go into the parenthesis.
positive eight minus nine, is negative one.
equals zero
now we write the first part, as "x" minus three squared
minus one equals zero
again, we are trying to solve a quadratic equation here.
what we do at this point is you now simply
add the one to both sides
so "x" minus three squared ,
equals positive one
and the whole point of solving a quadratic equation by completing the square,
is getting to the step we are at right now
'cause what we are going to do is we are going to take the square root of
both sides, so if we take the square root of both sides, "x" minus three
squared,
equals the square root of the right side
okay, so once we take the square roots, we should put a positive
or negative on one side
on the left, if we take the square root,
of a quantity squared,
you're left with the inside, "x" minus 3
equals either positive, or negative one.
so now we get our two separate equations that we now have to solve
one of the equations we will
have to solve will be x minus 3
equals positive one
and the other equation we'll have to solve
will be x minus three equals negative one.
so well will simply add three in both cases
and we'll get "X" equals positive four. as one of our solutions
if you add positive three to the other side,
we'll get "X" equals positive two
as our other solution
and you can check that if you plug a
two and four into the original equation,
you will get zero.
alright, so this will be example one
in my extra example I will change the coefficient
on the x squared
to make it a little more tedious
stick around if you need to see that example, it should be close by