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Simplifying R(t) = 60t + 50t + -1t2 Multiply R * t tR = 60t + 50t + -1t2 Combine like terms: 60t + 50t = 110t tR = 110t + -1t2 Solving tR = 110t + -1t2 Solving for variable 't'. Reorder the terms: -110t + tR + t2 = 110t + -1t2 + -110t + t2 Reorder the terms: -110t + tR + t2 = 110t + -110t + -1t2 + t2 Combine like terms: 110t + -110t = 0 -110t + tR + t2 = 0 + -1t2 + t2 -110t + tR + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -110t + tR + t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-110 + R + t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-110 + R + t)' equal to zero and attempt to solve: Simplifying -110 + R + t = 0 Solving -110 + R + t = 0 Move all terms containing t to the left, all other terms to the right. Add '110' to each side of the equation. -110 + R + 110 + t = 0 + 110 Reorder the terms: -110 + 110 + R + t = 0 + 110 Combine like terms: -110 + 110 = 0 0 + R + t = 0 + 110 R + t = 0 + 110 Combine like terms: 0 + 110 = 110 R + t = 110 Add '-1R' to each side of the equation. R + -1R + t = 110 + -1R Combine like terms: R + -1R = 0 0 + t = 110 + -1R t = 110 + -1R Simplifying t = 110 + -1RSolution
t = {0, 110 + -1R}
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