−20cos 2 x−3cosx=−2 answer in decimals

Well, first of all, the equation in your question isn't clear.  I decided that you intended to write the equation

-20 cos²(x) - 3 cos(x) = -2

If this is not the correct equation, then you should stop reading right here.  Everything else from here on is nonsense, and you should report my answer.

= = = = =

If that IS the correct equation, then ...

Multiply each side by -1 . . . 20 cos²(x) + 3 cos(x) = 2

Subtract 2 from each side . . . 20 cos²(x) + 3 cos(x) - 2 = 0

This is a quadratic equation in 'cos(x)' .  I messed around for a while trying to factor it, and then I gave up and used the Quadratic Formula.

Like any other quadratic equation, this one has two roots:

(1).  cos(x) = -119/40  or  -0.475

(2).  cos(x) = 7/40  or  0.175

For the first one, the angle 'x' is 118.36°  or  241.64°

For the second one, the angle 'x' is 79.92°  or  280.08°

So the original equation ... the one with all the cosines in it ... actually has four (4) solutions.

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step-by-step explanation: