to solve this by completing the square
first add the constant to the other side
in this case adding one leaves us with x
squared plus 6x
now leave some space for the special
number equals one plus now to determine
the special number you look at the
coefficient of the X in this case six
take that divide it by two and then
whatever you get you want to square it
in this case three squared is nine so
what I'm going to do is add nine to both
sides and the equation there and then
what's left on the left side should be a
perfect square let's see x and x nine
factors into three times three adds up
to six if they're both positive so you
can see we got a perfect square on the
left side X plus three squared equals
ten so now we can extract the root take
the square root of both sides don't
forget when you do that you need the
plus or minus and that leaves us in this
particular case with X plus three equals
plus or minus the square root of 10 and
then subtracting the three on both sides
we could solve for x x equals negative
three plus or minus the square root of
ten so we got two solutions here okay so
my solutions are negative three minus
the square root of 10 and negative three
plus the square root of 10
