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Simplifying 2cos2(2x + 40) + 5sin(2x + 40) + -4 = 0 Reorder the terms: 2cos2(40 + 2x) + 5sin(2x + 40) + -4 = 0 (40 * 2cos2 + 2x * 2cos2) + 5sin(2x + 40) + -4 = 0 (80cos2 + 4cos2x) + 5sin(2x + 40) + -4 = 0 Reorder the terms: 80cos2 + 4cos2x + 5ins(40 + 2x) + -4 = 0 80cos2 + 4cos2x + (40 * 5ins + 2x * 5ins) + -4 = 0 80cos2 + 4cos2x + (200ins + 10insx) + -4 = 0 Reorder the terms: -4 + 80cos2 + 4cos2x + 200ins + 10insx = 0 Solving -4 + 80cos2 + 4cos2x + 200ins + 10insx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 80cos2 + 4cos2x + 200ins + 4 + 10insx = 0 + 4 Reorder the terms: -4 + 4 + 80cos2 + 4cos2x + 200ins + 10insx = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 80cos2 + 4cos2x + 200ins + 10insx = 0 + 4 80cos2 + 4cos2x + 200ins + 10insx = 0 + 4 Combine like terms: 0 + 4 = 4 80cos2 + 4cos2x + 200ins + 10insx = 4 Add '-200ins' to each side of the equation. 80cos2 + 4cos2x + 200ins + -200ins + 10insx = 4 + -200ins Combine like terms: 200ins + -200ins = 0 80cos2 + 4cos2x + 0 + 10insx = 4 + -200ins 80cos2 + 4cos2x + 10insx = 4 + -200ins Add '-10insx' to each side of the equation. 80cos2 + 4cos2x + 10insx + -10insx = 4 + -200ins + -10insx Combine like terms: 10insx + -10insx = 0 80cos2 + 4cos2x + 0 = 4 + -200ins + -10insx 80cos2 + 4cos2x = 4 + -200ins + -10insx Reorder the terms: -4 + 80cos2 + 4cos2x + 200ins + 10insx = 4 + -200ins + -10insx + -4 + 200ins + 10insx Reorder the terms: -4 + 80cos2 + 4cos2x + 200ins + 10insx = 4 + -4 + -200ins + 200ins + -10insx + 10insx Combine like terms: 4 + -4 = 0 -4 + 80cos2 + 4cos2x + 200ins + 10insx = 0 + -200ins + 200ins + -10insx + 10insx -4 + 80cos2 + 4cos2x + 200ins + 10insx = -200ins + 200ins + -10insx + 10insx Combine like terms: -200ins + 200ins = 0 -4 + 80cos2 + 4cos2x + 200ins + 10insx = 0 + -10insx + 10insx -4 + 80cos2 + 4cos2x + 200ins + 10insx = -10insx + 10insx Combine like terms: -10insx + 10insx = 0 -4 + 80cos2 + 4cos2x + 200ins + 10insx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 40cos2 + 2cos2x + 100ins + 5insx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 40cos2 + 2cos2x + 100ins + 5insx)' equal to zero and attempt to solve: Simplifying -2 + 40cos2 + 2cos2x + 100ins + 5insx = 0 Solving -2 + 40cos2 + 2cos2x + 100ins + 5insx = 0 Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 40cos2 + 2cos2x + 100ins + 2 + 5insx = 0 + 2 Reorder the terms: -2 + 2 + 40cos2 + 2cos2x + 100ins + 5insx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 40cos2 + 2cos2x + 100ins + 5insx = 0 + 2 40cos2 + 2cos2x + 100ins + 5insx = 0 + 2 Combine like terms: 0 + 2 = 2 40cos2 + 2cos2x + 100ins + 5insx = 2 Add '-100ins' to each side of the equation. 40cos2 + 2cos2x + 100ins + -100ins + 5insx = 2 + -100ins Combine like terms: 100ins + -100ins = 0 40cos2 + 2cos2x + 0 + 5insx = 2 + -100ins 40cos2 + 2cos2x + 5insx = 2 + -100ins Add '-5insx' to each side of the equation. 40cos2 + 2cos2x + 5insx + -5insx = 2 + -100ins + -5insx Combine like terms: 5insx + -5insx = 0 40cos2 + 2cos2x + 0 = 2 + -100ins + -5insx 40cos2 + 2cos2x = 2 + -100ins + -5insx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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