SOLUTION: cos^2(x)+3cos(x)-1=0

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Question 1150592: cos^2(x)+3cos(x)-1=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cos%5E2%28x%29%2B3cos%28x%29-1=0
Let cos%28x+%29=u
u%5E2%2B3u-1=0

For a quadratic equation of the form ax%5E2%2Bbx%2Bc=0 the solutions are:
x%5B1%2C2%5D=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
in your case a=1, b=3, c=-1
u%5B1%2C2%5D=%28-3%2B-sqrt%283%5E2-4%2A1%28-1%29%29%29%2F2%2A1
u%5B1%2C2%5D=%28-3%2B-sqrt%289%2B4%29%29%2F2
u%5B1%2C2%5D=%28-3%2B-sqrt%2813%29%29%2F2
u%5B1%5D=%28-3%2Bsqrt%2813%29%29%2F2+ and u%5B2%5D=%28-3-sqrt%2813%29%29%2F2
Substitute back u=+cos++%28x+%29:
cos++%28x+%29=%28-3%2Bsqrt%2813%29%29%2F2=> x=+arccos++%28%28-3%2Bsqrt%2813%29%29%2F2%29%2B2pi%2An , x=+2pi-+arccos++%28%28-3%2Bsqrt%2813%29%29%2F2%29%2B2pi%2An
or
cos++%28x+%29=%28-3-sqrt%2813%29%29%2F2=> none, so, disregard it

solutions in decimal form
x=1.26319++%2B2+pi+%2An
x=2pi+-1.26319+%2B2pi%2A+n