00:01
Here we have the quadratic inequality x squared plus 8 x is greater than negative 15.
00:06
In order to solve this, i need to start by making sure all my terms are on one side of the inequality symbol.
00:13
So i'm going to add 15 to both sides.
00:18
Now i'm going to solve the associated quadratic equation.
00:22
So i'm going to turn the inequality symbol to an equal sign and then solve.
00:27
This is a quadratic that i can solve by factoring.
00:30
So i know i'm looking for two numbers that multiply to 15 and that add to 8.
00:37
Those two numbers are going to be 5 and 3.
00:40
So we know our quadratic is going to factor to an x plus 3 times x plus 5 equals 0.
00:48
From here i can set each factor equal to 0 and solve for x.
00:55
This gives me that x equals negative 3 and x equals negative 5.
01:02
These aren't my solutions, though.
01:04
These are what are called my critical points, which represent the endpoints of intervals in my solution.
01:10
I'm going to use the critical points to plug into my original inequality, which is going to allow me to solve this inequality and find my solution set.
01:23
So what i'm going to do is label my critical points on the number line, and then i'm going to plug in a value in each interval.
01:30
So i'm going to plug in negative 6 .5.
01:32
Negative 4 and 0.
01:37
So let's start by plugging in negative 6 to my original inequality.
01:41
So that gives us negative 6 squared plus 8 times negative 6 is greater than negative 15.
01:49
So that is going to give us 36 minus 48 is greater than negative 15, which gives us negative 12 is greater than negative 15...