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Simplifying 5acosx + 12asenx + -5bsenx + 12bcosx = 0 Reorder the terms: 5acosx + 12aensx + 12bcosx + -5bensx = 0 Solving 5acosx + 12aensx + 12bcosx + -5bensx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12bcosx' to each side of the equation. 5acosx + 12aensx + 12bcosx + -12bcosx + -5bensx = 0 + -12bcosx Combine like terms: 12bcosx + -12bcosx = 0 5acosx + 12aensx + 0 + -5bensx = 0 + -12bcosx 5acosx + 12aensx + -5bensx = 0 + -12bcosx Remove the zero: 5acosx + 12aensx + -5bensx = -12bcosx Add '5bensx' to each side of the equation. 5acosx + 12aensx + -5bensx + 5bensx = -12bcosx + 5bensx Combine like terms: -5bensx + 5bensx = 0 5acosx + 12aensx + 0 = -12bcosx + 5bensx 5acosx + 12aensx = -12bcosx + 5bensx Reorder the terms: 5acosx + 12aensx + 12bcosx + -5bensx = -12bcosx + 12bcosx + 5bensx + -5bensx Combine like terms: -12bcosx + 12bcosx = 0 5acosx + 12aensx + 12bcosx + -5bensx = 0 + 5bensx + -5bensx 5acosx + 12aensx + 12bcosx + -5bensx = 5bensx + -5bensx Combine like terms: 5bensx + -5bensx = 0 5acosx + 12aensx + 12bcosx + -5bensx = 0 Factor out the Greatest Common Factor (GCF), 'sx'. sx(5aco + 12aen + 12bco + -5ben) = 0Subproblem 1
Set the factor 'sx' equal to zero and attempt to solve: Simplifying sx = 0 Solving sx = 0 Move all terms containing a to the left, all other terms to the right. Add '-1sx' to each side of the equation. sx + -1sx = 0 + -1sx Remove the zero: 0 = -1sx Simplifying 0 = -1sx 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 '(5aco + 12aen + 12bco + -5ben)' equal to zero and attempt to solve: Simplifying 5aco + 12aen + 12bco + -5ben = 0 Solving 5aco + 12aen + 12bco + -5ben = 0 Move all terms containing a to the left, all other terms to the right. Add '-12bco' to each side of the equation. 5aco + 12aen + 12bco + -12bco + -5ben = 0 + -12bco Combine like terms: 12bco + -12bco = 0 5aco + 12aen + 0 + -5ben = 0 + -12bco 5aco + 12aen + -5ben = 0 + -12bco Remove the zero: 5aco + 12aen + -5ben = -12bco Add '5ben' to each side of the equation. 5aco + 12aen + -5ben + 5ben = -12bco + 5ben Combine like terms: -5ben + 5ben = 0 5aco + 12aen + 0 = -12bco + 5ben 5aco + 12aen = -12bco + 5ben 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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