00:01
We want to solve the equation the square root of 2r plus 11 minus the square root of 5r plus 1 equals negative 1.
00:07
We're going to add one of the radicals to the right -hand side.
00:11
So on the left, this is the square root of 2r plus 11, and now on the right it'll be negative 1 plus the square root.
00:19
Now we can square both sides so that we're counteracting the square root, and we have 2r plus 11 on the left, and now we square negative 1 to get 1, multiply a and b together and double.
00:33
So it would be minus 2 times a square to 5r plus 1, and then double the b term.
00:40
That is 5r, excuse me square of the b term, 5r plus 1.
00:46
All right.
00:47
Now we want to work on isolating the radical that we still have.
00:52
Let's say this 1 plus 1 is 2, and we can subtract 2 to both sides.
01:05
We can subtract 5r to both sides.
01:12
You can divide both sides by negative 2, and now we can square both sides, now that the radicals isolated.
01:29
And we have just 5r plus 1 on the right, and on the left you square the numerator, which would be square, multiply is negative 27r, and negative 27 times 2 is negative 54, so minus 54r plus 81, over 2 squared, which is 4.
01:55
Now i'm going to multiply both sides of the equation by 4 and becomes 4 times 5r plus 1 or 20 r plus 4.
02:12
Subtract, since this is a quadratic, everything's on one side of the equation.
02:17
So it would be 9r squared, subtract 20 r to get negative 74r.
02:23
And subtract 4, 81 minus 4 is 77.
02:27
And that would be plus 77.
02:32
Okay.
02:34
Now let's use the quadratic formula.
02:37
Opposite b plus or minus the square root of b squared minus 4 a c all over to a.
02:59
So we have 74 plus or minus the square root of negative 74 squared minus 4 times 9 times 77 is 2704.
03:10
The square of that is 52.
03:14
Over 18...