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Simplifying 5ct4 + -5ck4 = 0 Reorder the terms: -5ck4 + 5ct4 = 0 Solving -5ck4 + 5ct4 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '5c'. 5c(-1k4 + t4) = 0 Factor a difference between two squares. 5c((k2 + t2)(-1k2 + t2)) = 0 Factor a difference between two squares. 5c((k2 + t2)((k + t)(-1k + t))) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(k2 + t2)' equal to zero and attempt to solve: Simplifying k2 + t2 = 0 Solving k2 + t2 = 0 Move all terms containing c to the left, all other terms to the right. Add '-1k2' to each side of the equation. k2 + -1k2 + t2 = 0 + -1k2 Combine like terms: k2 + -1k2 = 0 0 + t2 = 0 + -1k2 t2 = 0 + -1k2 Remove the zero: t2 = -1k2 Add '-1t2' to each side of the equation. t2 + -1t2 = -1k2 + -1t2 Combine like terms: t2 + -1t2 = 0 0 = -1k2 + -1t2 Simplifying 0 = -1k2 + -1t2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(k + t)' equal to zero and attempt to solve: Simplifying k + t = 0 Solving k + t = 0 Move all terms containing c to the left, all other terms to the right. Add '-1k' to each side of the equation. k + -1k + t = 0 + -1k Combine like terms: k + -1k = 0 0 + t = 0 + -1k t = 0 + -1k Remove the zero: t = -1k Add '-1t' to each side of the equation. t + -1t = -1k + -1t Combine like terms: t + -1t = 0 0 = -1k + -1t Simplifying 0 = -1k + -1t The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(-1k + t)' equal to zero and attempt to solve: Simplifying -1k + t = 0 Solving -1k + t = 0 Move all terms containing c to the left, all other terms to the right. Add 'k' to each side of the equation. -1k + k + t = 0 + k Combine like terms: -1k + k = 0 0 + t = 0 + k t = 0 + k Remove the zero: t = k Add '-1t' to each side of the equation. t + -1t = k + -1t Combine like terms: t + -1t = 0 0 = k + -1t Simplifying 0 = k + -1t The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
c = {0}
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