Solve the equation for all values of x between 0 and 180 degrees. 2sin^2 x + 3cos x = 0 .

We have to solve 2*(sin x)^2 + 3*cos x = 0 for values of x
in the interval {0, 180}

2*(sin x)^2 + 3*cos x =
0

=> 2*(1 - (cos x)^2) + 3*cos x =
0

=> 2 - 2*(cos x)^2 + 3*cos x =
0

=> 2*(cos x)^2 - 3*cos x - 2 =
0

=> 2*(cos x)^2 - 4*cos x + cos x - 2 =
0

=> 2*(cos x)[ cos x - 2] + 1[cos x - 2] =
0

=> [2*(cos x) + 1][ cos x - 2] =
0

[2*(cos x) + 1] =
0

=> 2*cos x =
-1

=> cos x =
-1/2

=> x = arc
cos(-1/2)

=> x = 120
degrees

cos x - 2 =
0

=> cos x = 2 which is not
possible

The required solution of the
equation is x = 120 degrees