SOLUTION: Please help solve other equation: sqrt(8x+1)= x+2.

Algebra ->  Radicals -> SOLUTION: Please help solve other equation: sqrt(8x+1)= x+2.      Log On


   

Question 370843: Please help solve other equation: sqrt(8x+1)= x+2.
Answer by 949homeworkhelp(1) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(8x+1)= x+2

8x%2B1=%28x%2B2%29%5E2 eliminate the sq. root by squaring the other side
8x%2B1=x%5E2%2B2%5E2
8x%2B1+=+x%5E2+%2B+4
-x%5E2%2B8x-3+=+0 bring everything to one side.
use quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B8x%2B-3+=+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=%288%29%5E2-4%2A-1%2A-3=52.

Discriminant d=52 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+52+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+52+%29%29%2F2%5C-1+=+0.394448724536011
x%5B2%5D+=+%28-%288%29-sqrt%28+52+%29%29%2F2%5C-1+=+7.60555127546399

Quadratic expression -1x%5E2%2B8x%2B-3 can be factored:
-1x%5E2%2B8x%2B-3+=+-1%28x-0.394448724536011%29%2A%28x-7.60555127546399%29
Again, the answer is: 0.394448724536011, 7.60555127546399. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B8%2Ax%2B-3+%29