SOLUTION: Solve the equation: 6x = sqrt(24+12x) x = -3/2, 1 x = 3/2, 1 x = 2/3, 1 x = -2/3, 1

Algebra ->  Equations -> SOLUTION: Solve the equation: 6x = sqrt(24+12x) x = -3/2, 1 x = 3/2, 1 x = 2/3, 1 x = -2/3, 1      Log On


   

Question 1039579: Solve the equation:
6x = sqrt(24+12x)
x = -3/2, 1
x = 3/2, 1
x = 2/3, 1
x = -2/3, 1
Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!
[Note: The code you used doesn't work here.
Use html or just ordinary writing with no code.
Or use the special code of this site]

6x=sqrt%2824%2B12x%29

Square both sides:

%286x%29%5E2=%28sqrt%2824%2B12x%29%29%5E2

36x%5E2=24%2B12x

Get 0 on the right and left side in descending
order:

36x%5E2-12x-24=0

Divide every term on both sides by 12

3x%5E2-x-2=0

Factor the left side:

%283x%2B2%29%28x-1%29=0

Use the zero-factor property:



Checking x=-2%2F3 in original:

6x=sqrt%2824%2B12x%29
6%28-2%2F3%29=sqrt%2824%2B12%28-2%2F3%29%29
-4=sqrt%2824-8%29
-4=sqrt%2816%29
-4=4

False, so -2/3 is not a solution.

Checking x=1 in original:

6x=sqrt%2824%2B12x%29
6%281%29=sqrt%2824%2B12%281%29%29
6=sqrt%2824%2B12%29
6=sqrt%2836%29
6=6

True, so the only solution is x=1.
So none of the answers you listed are
correct because they all allow something
other than 1 to be a solution.

Edwin