SOLUTION: I don't understand the steps of solving this kind of problem.Never did these kinds before. 1 plus the sqrt of 2x+1 = 3x-8 I hope that you are able to understand what I wrote he

Algebra ->  Square-cubic-other-roots -> SOLUTION: I don't understand the steps of solving this kind of problem.Never did these kinds before. 1 plus the sqrt of 2x+1 = 3x-8 I hope that you are able to understand what I wrote he      Log On


   

Question 337711: I don't understand the steps of solving this kind of problem.Never did these kinds before.
1 plus the sqrt of 2x+1 = 3x-8
I hope that you are able to understand what I wrote here.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
1 plus the sqrt of 2x+1 = 3x-8
1%2Bsqrt%282x%2B1%29+=+3x+-8+
Subtracting 1 from both sides:
sqrt%282x%2B1%29+=+3x+-9+
Square both sides:
+2x%2B1+=+%283x-9%29%5E2+
+2x%2B1+=+%283x-9%29%283x-9%29+
+2x%2B1+=+9x%5E2-27x-27x%2B81+
+2x%2B1+=+9x%5E2-54x%2B81+
+1+=+9x%5E2-56x%2B81+
+0+=+9x%5E2-56x%2B80+
Applying quadratic formula we get:
x = {4, 2.22}
Plug both back in to check for "extraneous" solutions. Doing so, we eliminate the 2.22 leaving us with:
x = 4
.
Details of quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-56x%2B80+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-56%29%5E2-4%2A9%2A80=256.

Discriminant d=256 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--56%2B-sqrt%28+256+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-56%29%2Bsqrt%28+256+%29%29%2F2%5C9+=+4
x%5B2%5D+=+%28-%28-56%29-sqrt%28+256+%29%29%2F2%5C9+=+2.22222222222222

Quadratic expression 9x%5E2%2B-56x%2B80 can be factored:
9x%5E2%2B-56x%2B80+=+9%28x-4%29%2A%28x-2.22222222222222%29
Again, the answer is: 4, 2.22222222222222. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-56%2Ax%2B80+%29