now there's a number of ways to solve
this equation certainly we can multiply
this all out put it in standard form and
then refactor to even use the quadratic
formula but here I'm going to use a a
substitution here I'm going to let u
equal X plus 2 when u squared would
certainly be X plus 2 squared and that's
what we have here so u squared minus 2
times u plus 2 has to equal 0 so what's
left and is really just a quadratic
now this quadratic equation doesn't
factor so I'm gonna have to use the
quadratic formula where a is 1 B is
negative 2 and C is 2 so here's the two
solutions using the quadratic formula
but the variable here is U so u equals
negative B in this case negative
negative 2 plus or minus the square root
B squared minus 4 times a times C all
over 2a
okay simplifying negative negative 2 is
just positive 2 plus or minus the square
root 4 minus 8 all over 2 4 times 2 is 8
so notice here the discriminant is
negative so inside there I have a
negative 4 that tells me I'm gonna get
two complex solutions okay so 2 plus or
minus the square root of negative 4 is
2i all over 2 ok square root of 4 is 2
and the square root of negative 1 is I
simplifying we're gonna have two over 2
plus or minus 2i over to remember that 2
is a common denominator so we certainly
want to divide both of those terms by 2
and that'll leave us with 1 plus or
minus I okay so we got two solutions for
u u equals 1 minus I or u equals 1 plus
I we're solving for x at this point we
have to back substitute let's remember
X plus 2 is equal to u so back
substituting X plus 2 then should equal
1 minus I or X plus 2 should equal 1
plus I and then to finish this off let's
just solve for X here by simply
subtracting 2 so for one of the
solutions it happens to be x equals
negative 1 minus i for the other
solution subtracting 2 i'm left with x
equals negative 1 plus i so two
solutions here negative 1 plus or minus
I so that's how you do it using
substitution try it another way try to
solve this by multiplying it out putting
it in standard form then using the
quadratic form the see that you really
do get the same answer
