SOLUTION: sqrt5x-1=-sqrtx+2+3

Algebra ->  Radicals -> SOLUTION: sqrt5x-1=-sqrtx+2+3      Log On


   

Question 1108200: sqrt5x-1=-sqrtx+2+3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt5x-1=-sqrtx+2+3
===================
sqrt(5x) - 1 = -sqrt(x) +2 + 3
sqrt(5x) - 1 = -sqrt(x) + 5
sqrt(5x) = -sqrt(x) + 6
5x = x - 12sqrt(x) + 36
4x - 36 = -12sqrt(x)
x - 9 = -3sqrt(x)
x^2 - 18x + 81 = 9x
x^2 - 27x + 81 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-27x%2B81+=+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=%28-27%29%5E2-4%2A1%2A81=405.

Discriminant d=405 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+405+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+405+%29%29%2F2%5C1+=+23.5623058987491
x%5B2%5D+=+%28-%28-27%29-sqrt%28+405+%29%29%2F2%5C1+=+3.43769410125095

Quadratic expression 1x%5E2%2B-27x%2B81 can be factored:
1x%5E2%2B-27x%2B81+=+%28x-23.5623058987491%29%2A%28x-3.43769410125095%29
Again, the answer is: 23.5623058987491, 3.43769410125095. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-27%2Ax%2B81+%29