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Simplifying 24c2 + -26ct + -70t2 = 0 Reorder the terms: -26ct + 24c2 + -70t2 = 0 Solving -26ct + 24c2 + -70t2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13ct + 12c2 + -35t2) = 0 Factor a trinomial. 2((3c + -7t)(4c + 5t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3c + -7t)' equal to zero and attempt to solve: Simplifying 3c + -7t = 0 Solving 3c + -7t = 0 Move all terms containing c to the left, all other terms to the right. Add '7t' to each side of the equation. 3c + -7t + 7t = 0 + 7t Combine like terms: -7t + 7t = 0 3c + 0 = 0 + 7t 3c = 0 + 7t Remove the zero: 3c = 7t Divide each side by '3'. c = 2.333333333t Simplifying c = 2.333333333tSubproblem 2
Set the factor '(4c + 5t)' equal to zero and attempt to solve: Simplifying 4c + 5t = 0 Solving 4c + 5t = 0 Move all terms containing c to the left, all other terms to the right. Add '-5t' to each side of the equation. 4c + 5t + -5t = 0 + -5t Combine like terms: 5t + -5t = 0 4c + 0 = 0 + -5t 4c = 0 + -5t Remove the zero: 4c = -5t Divide each side by '4'. c = -1.25t Simplifying c = -1.25tSolution
c = {2.333333333t, -1.25t}
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