I'm going to solve this quadratic
equation by completing the square the
first step is to add the constant to the
other side that'll leave us with x
squared minus 2x now leave some space
because we're going to add a very
special number to both sides now to
complete the square you always look at
the coefficient of your X term in this
case the coefficient there is negative 2
you want to take that number divide it
by 2 and then square it so in this case
when I do that I get negative 1 squared
or 1 so the special number I'm going to
add to both sides is 1 when you do that
the left side should be a perfect square
let's see x times X 1 factors is 1 times
1 1 1 add up to negative 2 if they're
both negative so see that you get a
perfect square on the left side on the
right side here we get 9 so that leaves
us with X minus 1 squared equals 9 so at
this point in the process we can extract
the root let's take the square root of
both sides don't forget when you do that
you need to remember to put in the plus
or minus leaves us with X minus 1 equals
plus or minus 3 when I add 1 to both
sides I get x equals 1 plus or minus 3
so here we get 2 solutions when I use
minus 1 minus 3 is negative 2
or when I use the plus 1 plus 3 is 4
so notice we did get two solutions
negative 2 & 4 you can certainly plug
those into the original to see if they
work or solve the original by factoring
you should get the same answer
