00:02
Let's start this solving process by multiplying both sides of the equation by 2.
00:08
That'll give us e to the x plus e to the negative x equals 6.
00:15
We have a hint to multiply both sides of the equation by e to the x.
00:23
That would give us e to the 2x because e to the x times e to the x is e to the x plus x, which is 2x, plus e to the 0 because x plus negative x.
00:36
X is 0 and e to the 0 is 1.
00:42
Now we do have a quadratic in form so i'm going to subtract the 6 e to the x so that we're equal to 0.
00:53
Nothing multiplies to 1 and adds to negative 6 here but that just is an indicator that we'll use the quadratic formula.
01:02
We're going to let u be e to the x so we have u squared minus 6 u plus 1 and that'll be easier to deal with the quadratic.
01:12
Formula, which is, in this case, u would equal negative b plus or minus the square root of b squared minus 4a, c all over 2a.
01:27
In this instance, a is going to equal 1, b negative 6, and c positive 1.
01:34
So we have negative b plus or minus the square root of b squared minus 4ac all over 2a.
01:47
Negative of negative 6 is 6.
01:52
Negative 6 squared is 36 minus 4 is 32...