2sin^2(pi+x)-5cos(pi/2+x)+2=0

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To solve this equation for x, we can use trigonometric identities to simplify it:

2sin^2(pi+x) - 5cos(pi/2+x) + 2 = 0

Using the trigonometric identity sin^2(x) = 1 - cos^2(x), we can rewrite the equation as:

2(1 - cos^2(pi+x)) - 5cos(pi/2+x) + 2 = 0

Expanding and simplifying:

2 - 2cos^2(pi+x) - 5cos(pi/2)cos(x) + 5sin(pi/2)sin(x) + 2 = 0
2 - 2cos^2(pi+x) - 5(0)cos(x) + 5(1)sin(x) + 2 = 0
2 - 2cos^2(pi+x) + 5sin(x) + 2 = 0
4 - 2cos^2(pi+x) + 5sin(x) = 0
2 - cos^2(pi+x) + 5sin(x) = 0
cos^2(pi+x) - 5sin(x) = 2

Using the identity cos(x) = sin(x + pi/2), we can further simplify the equation:

sin(pi/2 + x)^2 - 5sin(x) = 2
sin^2(pi/2)cos^2(x) + 2sin(pi/2)cos(x) + cos^2(pi/2) - 5sin(x) = 2
1 - 5sin(x) = 2
-5sin(x) = 1
sin(x) = -1/5

Therefore, the solution to the equation 2sin^2(pi+x) - 5cos(pi/2+x) + 2 = 0 is x = sin^(-1)(-1/5) + 2kpi, where k is an integer.