Guest, I am sorry to hear that.
It is clear that your first statement is correct, and it is my mistake that I have not gone over the question carefully.
I have checked at the original site whether my answer is correct, and I have come to the conclusion that it is. If you are making fun of it because I have not directly included the answer, than I have nothing to say for you but answer-dependent. Otherwise, you will have to convince me that my process of solution is wrong.
Finally, I have a picture of my work of all the angles marked out accordingly to the given statements. I have confirmed repeatedly, and unless you can give convincing reasons to use the word ATROCIOUS and the Field MeTal, I will have to flag your response in the name of mis-accusing.
The picture is here:
The original site, in case you forgot it, is here: https://web2.0calc.com/questions/help-with-geometry_125
I'm sorry to tell that if you are trying to get a specific value for k, you can not since there are three variables and two equations!
However, if you are trying to express k in terms of X, that's great!
k = 3p, so 18p is 6k. Sub that into the first equation to get 10k = 1/4X, and from that you can complete the rest.
The stuff under square root needs to be bigger than 0.
We factor to get: -6(x^2-2x-3)>= 0, thus -6(x-3)(x+1) >= 0.
We can get rid of -6, but we need to change the sign. (x-3)(x+1) <= 0.
Two pairs of possibilities: x-3>= 0, x+1 <=0
and x-3 <= 0, x+1 >=0.
Simplify to get x>=3, x<=-1(which is impossible so we abandon it)
and x<=3, x>=-1(which makes sense)
Finally, the domain is [-1, 3]