SOLUTION: Two Problems Find all real solutions: 3x+√(x+1) = 49 x=___(Smaller answer) x=___(Larger answer) =========== ==== And solve for S 1/R = 1/S + 1/T S = ?

Algebra ->  Functions -> SOLUTION: Two Problems Find all real solutions: 3x+√(x+1) = 49 x=___(Smaller answer) x=___(Larger answer) =========== ==== And solve for S 1/R = 1/S + 1/T S = ?       Log On


   

Question 904485: Two Problems
Find all real solutions:
3x+√(x+1) = 49
x=___(Smaller answer)
x=___(Larger answer)
================
And solve for S
1/R = 1/S + 1/T
S = ?
Please explain how to solve both, thank you
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
3x+√(x+1) = 49
√(x+1) = (49 -3x) Squaring both sides
9x^2 - 295x + 2400 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-295x%2B2400+=+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=%28-295%29%5E2-4%2A9%2A2400=625.

Discriminant d=625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--295%2B-sqrt%28+625+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-295%29%2Bsqrt%28+625+%29%29%2F2%5C9+=+17.7777777777778
x%5B2%5D+=+%28-%28-295%29-sqrt%28+625+%29%29%2F2%5C9+=+15

Quadratic expression 9x%5E2%2B-295x%2B2400 can be factored:
9x%5E2%2B-295x%2B2400+=+9%28x-17.7777777777778%29%2A%28x-15%29
Again, the answer is: 17.7777777777778, 15. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-295%2Ax%2B2400+%29