SOLUTION: Here is my question: Find all possible solutions. Give your answeres in increasing order. sqrt(-3x+5)-5=9x Thanks so much!

Algebra ->  Radicals -> SOLUTION: Here is my question: Find all possible solutions. Give your answeres in increasing order. sqrt(-3x+5)-5=9x Thanks so much!      Log On


   

Question 287428: Here is my question:
Find all possible solutions. Give your answeres in increasing order.
sqrt(-3x+5)-5=9x
Thanks so much!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find all possible solutions. Give your answers in increasing order.
sqrt%28-3x%2B5%29-5+=9x
Add 5 to both sides
sqrt%28-3x%2B5%29=9x%2B5
square both sides:
-3x + 5 = (9x+5)^2
FOIL the right side
-3x + 5 = 81x^2 + 90x + 25
:
Write as quadratic equation
0 = 81x^2 + 90x + 3x + 25 - 5
81x^2 + 93x + 20 = 0
Use the quadratic equation to find x;
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem a=81; b=93; c=20
x+=+%28-93+%2B-+sqrt%2893%5E2+-+4%2A81%2A20+%29%29%2F%282%2A81%29+
:
x+=+%28-93+%2B-+sqrt%288649-6480+%29%29%2F162+
:
x+=+%28-93+%2B-+sqrt%282169+%29%29%2F162+
Two solutions
x+=+%28-93+%2B+46.5725%29%2F162+
:
x = %28-46.427%29%2F162
x = -.28659
and
x+=+%28-93+-+46.5725%29%2F162+
:
x = %28-139.5725%29%2F162
x = -.86156
:
Check both of these solutions in the original equation,
only x = -.28659 is a solution