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!

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) (Show Source): You can put this solution on YOUR website!

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:

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:

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.
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