SOLUTION: I am not having good luck with this answer. Please help!!! {{{2x-3=sqrt(30-7x)}}} I squared off the expression 2x-3 and used the FOIL method to get this: 4x-12x+9=30-7x I

Algebra ->  Radicals -> SOLUTION: I am not having good luck with this answer. Please help!!! {{{2x-3=sqrt(30-7x)}}} I squared off the expression 2x-3 and used the FOIL method to get this: 4x-12x+9=30-7x I      Log On


   

Question 992036: I am not having good luck with this answer. Please help!!!
2x-3=sqrt%2830-7x%29
I squared off the expression 2x-3 and used the FOIL method to get this:
4x-12x+9=30-7x I continue by subtracting 4x-12x to get -8x+9=30-7x. Here's where I think I lose it.
Somewhere I'm missing something because I keep getting x=21 but the answer key says {3}
Found 3 solutions by jim_thompson5910, macston, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x-3=sqrt%2830-7x%29


%282x-3%29%5E2=%28sqrt%2830-7x%29%29%5E2 Square both sides


%282x-3%29%5E2=30-7x Use the rule %28sqrt%28x%29%29%5E2+=+x


%282x-3%29%282x-3%29=30-7x Use the rule x%5E2=x%2Ax


4x%5E2-12x%2B9=30-7x FOIL the left side. This is where you made your mistake. You should have 4x%5E2 and not 4x


4x%5E2-12x%2B9-30%2B7x=0 Get everything to one side.


4x%5E2-5x-21=0 Combine like terms.


Next you use the quadratic formula to solve for x. I'll let you finish up.


Note: don't forget to check each possible answer back in the original equation.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
First step: Square both sides:
(2x-3)^2
.
FOIL:Multiply first terms:
2x%2A2x=4x%5E2 not 4x
.
Continued:
2x-3=sqrt%2830-7x%29
%282x-3%29%5E2=30-7x
4x%5E2-12x%2B9=30-7x
4x%5E2-5x-21=0
%284x%2B7%29%28x-3%29=0
4x%2B7=0 OR x-3=0
4x=-7 OR x=3
x=-7%2F4 OR x=3
The domain of the original is:
3%2F2<x<30%2F7
so -7/4 is eliminated, leaving:
.
ANSWER:x=3


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I am not having good luck with this answer. Please help!!!
2x-3=sqrt%2830-7x%29
I squared off the expression 2x-3 and used the FOIL method to get this:
4x-12x+9=30-7x I continue by subtracting 4x-12x to get -8x+9=30-7x. Here's where I think I lose it.
Somewhere I'm missing something because I keep getting x=21 but the answer key says {3} 
First error: %282x+-+3%29%5E2+=+4x%5E2+-+12x+%2B+9, not: 4x+-+12x+%2B+9. Major error!!