SOLUTION: I have to solve and check this equation: sqrt(2x)=-12. I believe it has no solution, but I don't know how to show my work!

Algebra ->  Radicals -> SOLUTION: I have to solve and check this equation: sqrt(2x)=-12. I believe it has no solution, but I don't know how to show my work!      Log On


   

Question 358121: I have to solve and check this equation: sqrt(2x)=-12. I believe it has no solution, but I don't know how to show my work!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%29=-12
You are right. A square root cannot be a negative number.

If this logic is insufficient "work", then you could proceed as if you didn't notice this inconsistency:
Square both sides:
%28sqrt%282x%29%29%5E2+=+%28-12%29%5E2
2x = 144
Divide both sides by 2:
x = 72

At this point it appears that we have a solution. But whenever you square both sides of an equation, like we have, you must check your answers. (Squaring both sides of an equation can introduce what a called "extraneous solutions". Extraneous solutions are solutions that work in the squared equation but not in the original equation.

Checking x = 72 in the original equation:
sqrt%282%2872%29%29=-12
sqrt%28144%29=-12
12+=+-12 and the check fails! x = 72 is an extraneous solution and must be rejected. Since we have rejected the only "solution", there are no solutions to your equation.