Here, the final solutions are 3 plus or minus 3 times the square root of 2.
Great work if you found those answers. The coefficient in front of this x
squared term is a 1, since it's not listed. So, a equals 1, b equals negative
6, and c equals negative 9. We substitute the values of a, b, and c into our
quadratic formula, being sure to use parenthesis around each of the values. So,
we'll have positive 6 for the negative of b, we'll have 36 for squaring b, and
then we'll have positive 36 for negative 4acC. Here, the denominator will just
be 2, 2 times 1. We have 36 plus 36 in our radical, so really, that's 2 times
36. I leave it like this since I can take the square root of 36, which is 6.
The 2 stays inside of our radical, and then we simplify it by dividing each of
these terms, 2 into 6 equals 3 and 2 into 6 radical 2 is 3 radical 2. Another
way to think about this is we could factor 2 from these two 6s, leaving us with
this numerator. We cancel the common factors that reduce to 1, leaving us with
3 plus or minus 3 root 2, our final solutions.
