2cos(0.5x)+3=-2x^2+x+10

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Solution for 2cos(0.5x)+3=-2x^2+x+10 equation:


Simplifying
2cos(0.5x) + 3 = -2x2 + x + 10

Remove parenthesis around (0.5x)
2cos * 0.5x + 3 = -2x2 + x + 10

Reorder the terms for easier multiplication:
2 * 0.5cos * x + 3 = -2x2 + x + 10

Multiply 2 * 0.5
1cos * x + 3 = -2x2 + x + 10

Multiply cos * x
1cosx + 3 = -2x2 + x + 10

Reorder the terms:
3 + 1cosx = -2x2 + x + 10

Reorder the terms:
3 + 1cosx = 10 + x + -2x2

Solving
3 + 1cosx = 10 + x + -2x2

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 1cosx = 10 + x + -3 + -2x2

Combine like terms: 3 + -3 = 0
0 + 1cosx = 10 + x + -3 + -2x2
1cosx = 10 + x + -3 + -2x2

Reorder the terms:
1cosx = 10 + -3 + x + -2x2

Combine like terms: 10 + -3 = 7
1cosx = 7 + x + -2x2

Divide each side by '1osx'.
c = 7o-1s-1x-1 + o-1s-1 + -2o-1s-1x

Simplifying
c = 7o-1s-1x-1 + o-1s-1 + -2o-1s-1x

Reorder the terms:
c = o-1s-1 + 7o-1s-1x-1 + -2o-1s-1x

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