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Simplifying sin(2x + -20) + cos(3x + 50) = 0 Reorder the terms: ins(-20 + 2x) + cos(3x + 50) = 0 (-20 * ins + 2x * ins) + cos(3x + 50) = 0 (-20ins + 2insx) + cos(3x + 50) = 0 Reorder the terms: -20ins + 2insx + cos(50 + 3x) = 0 -20ins + 2insx + (50 * cos + 3x * cos) = 0 -20ins + 2insx + (50cos + 3cosx) = 0 Reorder the terms: 50cos + 3cosx + -20ins + 2insx = 0 Solving 50cos + 3cosx + -20ins + 2insx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '20ins' to each side of the equation. 50cos + 3cosx + -20ins + 20ins + 2insx = 0 + 20ins Combine like terms: -20ins + 20ins = 0 50cos + 3cosx + 0 + 2insx = 0 + 20ins 50cos + 3cosx + 2insx = 0 + 20ins Remove the zero: 50cos + 3cosx + 2insx = 20ins Add '-2insx' to each side of the equation. 50cos + 3cosx + 2insx + -2insx = 20ins + -2insx Combine like terms: 2insx + -2insx = 0 50cos + 3cosx + 0 = 20ins + -2insx 50cos + 3cosx = 20ins + -2insx Reorder the terms: 50cos + 3cosx + -20ins + 2insx = 20ins + -20ins + -2insx + 2insx Combine like terms: 20ins + -20ins = 0 50cos + 3cosx + -20ins + 2insx = 0 + -2insx + 2insx 50cos + 3cosx + -20ins + 2insx = -2insx + 2insx Combine like terms: -2insx + 2insx = 0 50cos + 3cosx + -20ins + 2insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(50co + 3cox + -20in + 2inx) = 0Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing c to the left, all other terms to the right. Add '-1s' to each side of the equation. s + -1s = 0 + -1s Remove the zero: 0 = -1s Simplifying 0 = -1s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(50co + 3cox + -20in + 2inx)' equal to zero and attempt to solve: Simplifying 50co + 3cox + -20in + 2inx = 0 Solving 50co + 3cox + -20in + 2inx = 0 Move all terms containing c to the left, all other terms to the right. Add '20in' to each side of the equation. 50co + 3cox + -20in + 20in + 2inx = 0 + 20in Combine like terms: -20in + 20in = 0 50co + 3cox + 0 + 2inx = 0 + 20in 50co + 3cox + 2inx = 0 + 20in Remove the zero: 50co + 3cox + 2inx = 20in Add '-2inx' to each side of the equation. 50co + 3cox + 2inx + -2inx = 20in + -2inx Combine like terms: 2inx + -2inx = 0 50co + 3cox + 0 = 20in + -2inx 50co + 3cox = 20in + -2inx 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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