SOLUTION: 1. I need to figure out the soultion set for radical(3x+7)+ radical(x+6)=3. The number in parenthesis are actually supposed to be under the radical, I just don't have a button for

Algebra ->  Radicals -> SOLUTION: 1. I need to figure out the soultion set for radical(3x+7)+ radical(x+6)=3. The number in parenthesis are actually supposed to be under the radical, I just don't have a button for       Log On


   

Question 71909: 1. I need to figure out the soultion set for radical(3x+7)+ radical(x+6)=3. The number in parenthesis are actually supposed to be under the radical, I just don't have a button for that. So radical + a radical.
2. Find the domain of: x-2/radical(x+2)

Thank you,
Nikki
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. I need to figure out the solution set for radical(3x+7)+ radical(x+6)=3.
sqrt%283x%2B7%29+%2B+sqrt%28x%2B6%29 = 3
:
Subtract sqrt%28x%2B6%29 from both sides:
sqrt%283x%2B7%29 = 3 -sqrt%28x%2B6%29
:
Square both sides; FOIL (3-Sqrt(x+6))*(3-Sqrt(x+6):
3x + 7 = 9 - 6sqrt%28x-6%29 + (x+6)
:
3x + 7 = 9 - 6sqrt%28x-6%29 + x + 6
:
3x + 7 = 9 + 6 + x -6sqrt%28x%2B6%29
:
3x + 7 = 15 + x -6sqrt%28x%2B6%29
:
Get the radical on the right by itself:
3x - x + 7 - 15 = -6sqrt%28x%2B6%29
:
2x - 8 = -6sqrt%28x%2B6%29
:
Square both sides; FOIL (2x - 8)^2
4x^2 - 32x + 64 = +36(x+6)
4x^2 - 32x + 64 = 36x + 216
4x^2 - 32x - 36x + 64 - 216 = 0
4x^2 - 68x - 152 = 0
:
Simplify, divide equation by 4:
x^2 - 17x - 38 = 0
:
Factors to:
(x - 19)(x + 2) = 0
:
x = +19 and x = -2; only the x = -2 is a solution, check it for yourself
:
:
2. Find the domain of: x-2/radical(x+2)
%28x-2%29%2Fsqrt%28x%2B2%29
There are two no-no's to remember. You can't have 0 in the denominator and
you can have a negative result inside the radical: domain of: x > -2