# How do yo solve #2Cos^2(x) - 2sen(x) + 12 = 0# ?

##### 1 Answer

Mar 5, 2018

See explanation

#### Explanation:

We want to solve the equation

#2cos^2(x)-2sin(x)+12=0#

Use

#2(1-sin^2(x))-2sin(x)+12=0#

Simplify

#-2sin^2(x)-2sin(x)+14=0#

#=>sin^2(x)+sin(x)-7=0#

Let

#u^2+u-7=0#

#=>u=(-1+-sqrt(29))/2#

#=>sin(x)=(-1+-sqrt(29))/2#

So the equation have no solutions within the real numbers

because