What are the solutions to 2sin^2x+sinx-1=0?

sin x=30°,150°,-90

step-by-step explanation:

we let sin x be represented by the unknown a.

thus the equation becomes: 2a²+x-1=0

we find two terms that when multiplied give us -2, that is (ac)

but when added give 1 the value of b.

the two terms are: 2 and -1

2x²+2x-x-1=0

2x(x+1)-1(x+1)=0

factoring, we get: (2x-1)(x+1)=0

therefore 2x-1=0 or x+1=0

x=1/2   or -1.

thus sin x=1/2 or -1

between 0° and 360° the angles whose sine is 1/2 is 30° and 150°

while for -1 it is -90