here I want to solve this by completing
the square well the first step is to add
the 10 to both sides and that'll leave
you with negative 2x squared minus 8x
equals 10 now there's a little bit of a
problem when there's a coefficient from
the x squared term we need that
coefficient to be one in any case 2 has
no chance of being a perfect square so
when we factor out the two what's left
here is x squared minus 4x and we're
going to leave some space for that very
special number that completes the square
okay so now that the leading coefficient
is 1 we can look at our coefficient on
the X which in this case is negative 4
so you take that number you have to
divide it by two and then square it okay
so negative 4 divided by 2 is negative 2
when I square that I'm going to get 4 so
the magic number here is for to balance
this you would think we would add 4 on
the right side but in fact 2 is a factor
so if I were to actually distribute that
2 back in I'm really adding 8 to the
left side 2 times 4 is 8 so to balance
that out i'm going to add 8 on the right
side now that's that's tricky so make
sure you understand that what's left
here that trinomial should be a perfect
squared so equals 18 so let's see X and
X 4 factors 2 times 2 adds up to
negative 4 if they're both negative so
what's left here is 2 times X minus 2
squared equals 18 so we're ready to well
we're almost ready to extract the root
let's go ahead and divide by 2 and
that'll isolate the square in this case
X minus 2 squared then equals 9 so now
I'm ready to extract the root let's take
the square root of both sides don't
forget the plus or minus when you do
that leaves us with x minus 2 equals
plus or minus 3 adding 2 we get x equals
2 plus or minus 3 so this says X could
equal to minus 3 or
negative 1 or X could equal to plus 3
which is five so here we get the two
solutions negative one and five
