00:01
Here we have the quadratic inequality x squared minus plus 6x is less than negative 3.
00:06
To solve this, i'm going to do a process called completing the square, but first i'm going to change this to an equation and solve the associated quadratic equation before i solve the inequality.
00:19
To complete the square, i'm going to add a constant k to both sides of the equation.
00:26
K is going to equal b over 2 squared.
00:31
Where b is the coefficient of my linear term.
00:35
So 6 over 2 squared is just going to equal 9.
00:39
So i'm going to replace my k with 9.
00:45
After that, i can factor the left -hand side, which is going to factor to an x plus 3 quantity squared equals 6.
00:54
Then i can square root both sides, which is going to give me x plus 3 equals plus or minus squared of 6.
01:03
Then i subtract three from both sides.
01:06
So x equals negative 3 plus or minus root 6.
01:11
I'm going to plug this into my calculator and get the approximate decimal values.
01:19
So i'm going to get 5 .45 negative as well as negative .5 .5.
01:35
So for each of these values, i want to plug in a number.
01:41
That is in each interval.
01:43
So i'm gonna plug in negative six, negative five, and zero.
01:49
And i'm gonna plug these into my original inequality.
01:53
If i get a true statement, i know that that is part of my solution.
01:57
So i have to start, negative six squared plus six times negative six is less than negative three.
02:04
So 36 minus 36 is less than negative three...
