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Simplifying (2cosx + -1)(cosx + -5) = 0 Reorder the terms: (-1 + 2cosx)(cosx + -5) = 0 Reorder the terms: (-1 + 2cosx)(-5 + cosx) = 0 Multiply (-1 + 2cosx) * (-5 + cosx) (-1(-5 + cosx) + 2cosx * (-5 + cosx)) = 0 ((-5 * -1 + cosx * -1) + 2cosx * (-5 + cosx)) = 0 ((5 + -1cosx) + 2cosx * (-5 + cosx)) = 0 (5 + -1cosx + (-5 * 2cosx + cosx * 2cosx)) = 0 (5 + -1cosx + (-10cosx + 2c2o2s2x2)) = 0 Combine like terms: -1cosx + -10cosx = -11cosx (5 + -11cosx + 2c2o2s2x2) = 0 Solving 5 + -11cosx + 2c2o2s2x2 = 0 Solving for variable 'c'. Factor a trinomial. (1 + -2cosx)(5 + -1cosx) = 0Subproblem 1
Set the factor '(1 + -2cosx)' equal to zero and attempt to solve: Simplifying 1 + -2cosx = 0 Solving 1 + -2cosx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2cosx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2cosx = 0 + -1 -2cosx = 0 + -1 Combine like terms: 0 + -1 = -1 -2cosx = -1 Divide each side by '-2osx'. c = 0.5o-1s-1x-1 Simplifying c = 0.5o-1s-1x-1Subproblem 2
Set the factor '(5 + -1cosx)' equal to zero and attempt to solve: Simplifying 5 + -1cosx = 0 Solving 5 + -1cosx = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1cosx = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1cosx = 0 + -5 -1cosx = 0 + -5 Combine like terms: 0 + -5 = -5 -1cosx = -5 Divide each side by '-1osx'. c = 5o-1s-1x-1 Simplifying c = 5o-1s-1x-1Solution
c = {0.5o-1s-1x-1, 5o-1s-1x-1}
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