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Simplifying Tan(2x + 36) = tan(5x + 60) Reorder the terms: anT(36 + 2x) = tan(5x + 60) (36 * anT + 2x * anT) = tan(5x + 60) (36anT + 2anxT) = tan(5x + 60) Reorder the terms: 36anT + 2anxT = ant(60 + 5x) 36anT + 2anxT = (60 * ant + 5x * ant) 36anT + 2anxT = (60ant + 5antx) Solving 36anT + 2anxT = 60ant + 5antx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-60ant' to each side of the equation. 36anT + -60ant + 2anxT = 60ant + -60ant + 5antx Combine like terms: 60ant + -60ant = 0 36anT + -60ant + 2anxT = 0 + 5antx 36anT + -60ant + 2anxT = 5antx Add '-5antx' to each side of the equation. 36anT + -60ant + -5antx + 2anxT = 5antx + -5antx Combine like terms: 5antx + -5antx = 0 36anT + -60ant + -5antx + 2anxT = 0 Factor out the Greatest Common Factor (GCF), 'an'. an(36T + -60t + -5tx + 2xT) = 0Subproblem 1
Set the factor 'an' equal to zero and attempt to solve: Simplifying an = 0 Solving an = 0 Move all terms containing a to the left, all other terms to the right. Simplifying an = 0 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 '(36T + -60t + -5tx + 2xT)' equal to zero and attempt to solve: Simplifying 36T + -60t + -5tx + 2xT = 0 Solving 36T + -60t + -5tx + 2xT = 0 Move all terms containing a to the left, all other terms to the right. Add '-36T' to each side of the equation. 36T + -60t + -5tx + -36T + 2xT = 0 + -36T Reorder the terms: 36T + -36T + -60t + -5tx + 2xT = 0 + -36T Combine like terms: 36T + -36T = 0 0 + -60t + -5tx + 2xT = 0 + -36T -60t + -5tx + 2xT = 0 + -36T Remove the zero: -60t + -5tx + 2xT = -36T Add '60t' to each side of the equation. -60t + -5tx + 60t + 2xT = -36T + 60t Reorder the terms: -60t + 60t + -5tx + 2xT = -36T + 60t Combine like terms: -60t + 60t = 0 0 + -5tx + 2xT = -36T + 60t -5tx + 2xT = -36T + 60t Add '5tx' to each side of the equation. -5tx + 5tx + 2xT = -36T + 60t + 5tx Combine like terms: -5tx + 5tx = 0 0 + 2xT = -36T + 60t + 5tx 2xT = -36T + 60t + 5tx Add '-2xT' to each side of the equation. 2xT + -2xT = -36T + 60t + 5tx + -2xT Combine like terms: 2xT + -2xT = 0 0 = -36T + 60t + 5tx + -2xT Simplifying 0 = -36T + 60t + 5tx + -2xT 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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