SOLUTION: Hello I have absolutely struggled to find somewhere online that I can ask a question for free with no loopholes. Perhaps you would be able to help me with my small problem … I n

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello I have absolutely struggled to find somewhere online that I can ask a question for free with no loopholes. Perhaps you would be able to help me with my small problem … I n      Log On


   

Question 757206: Hello
I have absolutely struggled to find somewhere online that I can ask a question for free with no loopholes.
Perhaps you would be able to help me with my small problem …
I need to factorise the following quadratic
10sin^2 x (that is, 10 sin squared x) - 4sinx -5
I would really appreciate any help you could offer, as soon as possible.
Thanking you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
10y%5E2-4y-5 does not factorize into factors with rational coeficients.
10y%5E2-4y-5=0 can be solved using the quadratic formula to find
y=%284%2B-+216%29%2F20=%282+%2B-+54%29%2F10
Since those results satisfy -1%3Cy%3C1,
y=sin%28x%29 <--> x=arcsin%28y%29 would give you
x=arcsin%28%282+%2B-+54%29%2F10%29 as the two solutions for
10%28sin%28x%29%29%5E2-4sin%28x%29-5=0

On the other hand, since y%5E2-4y-5=%28y-5%29%28y%2B1%29
you can factorize %28sin%28x%29%29%5E2-4sin%28x%29-5 as
%28sin%28x%29%29%5E2-4sin%28x%29-5=%28sin%28x%29-5%29%28sin%28x%29%2B1%29