SOLUTION: I'm having trouble solving the following equation: square root of (3x-2) + square root of (2x+2) + 1 = 0. My major problem is coming from the fact that I'm getting stuck on isoloa

Algebra ->  Radicals -> SOLUTION: I'm having trouble solving the following equation: square root of (3x-2) + square root of (2x+2) + 1 = 0. My major problem is coming from the fact that I'm getting stuck on isoloa      Log On


   

Question 68462: I'm having trouble solving the following equation:
square root of (3x-2) + square root of (2x+2) + 1 = 0. My major problem is coming from the fact that I'm getting stuck on isoloating the radical, and I'm a little confused on where to place 1. Please help.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283x-2%29%2Bsqrt%282x%2B2%29%2B1=0 First thing that you want to do is get rid of the radicals by squaring both sides but before you do that you want to rearrange the terms on either side of the equal sign in a manner that simplifies that process. Sometimes you will need to square both sides more than once. Lets move the 1 to the right side of the equal sign by subtracting 1 from both sides:
sqrt%283x-2%29%2Bsqrt%282x%2B2%29=-1 Now lets square both sides:
%283x-2%29%2B2sqrt%28%282x%2B2%29%283x-2%29%29%2B%282x%2B2%29=%2B1 Lets collect like terms:
5x%2B2sqrt%28%282x%2B2%29%283x-2%29%29=%2B1 Now we will subtract 5x from both sides
2sqrt%28%282x%2B2%29%283x-2%29%29=1-5x Next lets square both sides again
4%282x%2B2%29%283x-2%29=1-10x%2B25x%5E2 Simplifying some we get
8%28x%2B1%29%283x-2%29=1-10x%2B25x%5E2 Next lets clear parens
24x%5E2%2B8x-16=1-10x%2B25x%5E2 Subtract 1 and 25x^2 from and add 10x to both sides
24x%5E2-25x%5E2%2B10x%2B8x-16-1=0 Collecting like terms:
-x%5E2%2B18x-17=0 Multiply through by -1
x%5E2-18x%2B17=0 ---------quadratic in standard form
This quadratic can be factored:
%28x-1%29%28x-17%29=0
x=1
and
x=17
ck
substitute 1 in the original equation:
sqrt%283x-2%29%2Bsqrt%282x%2B2%29%2B1=0 equals
sqrt%283-2%29%2Bsqrt%282%2B2%29%2B1=0 and this equals
sqrt%281%29%2Bsqrt%284%29%2B1=0
(+or-1)+(+or-2)+1=0
%2B1-2%2B1=0
0=0
verify that it also checks for x=17

Hope this helps---ptaylor