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Simplifying D(t) = 19t2 + -100t Multiply D * t tD = 19t2 + -100t Reorder the terms: tD = -100t + 19t2 Solving tD = -100t + 19t2 Solving for variable 't'. Reorder the terms: 100t + tD + -19t2 = -100t + 19t2 + 100t + -19t2 Reorder the terms: 100t + tD + -19t2 = -100t + 100t + 19t2 + -19t2 Combine like terms: -100t + 100t = 0 100t + tD + -19t2 = 0 + 19t2 + -19t2 100t + tD + -19t2 = 19t2 + -19t2 Combine like terms: 19t2 + -19t2 = 0 100t + tD + -19t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(100 + D + -19t) = 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 '(100 + D + -19t)' equal to zero and attempt to solve: Simplifying 100 + D + -19t = 0 Solving 100 + D + -19t = 0 Move all terms containing t to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + D + -100 + -19t = 0 + -100 Reorder the terms: 100 + -100 + D + -19t = 0 + -100 Combine like terms: 100 + -100 = 0 0 + D + -19t = 0 + -100 D + -19t = 0 + -100 Combine like terms: 0 + -100 = -100 D + -19t = -100 Add '-1D' to each side of the equation. D + -1D + -19t = -100 + -1D Combine like terms: D + -1D = 0 0 + -19t = -100 + -1D -19t = -100 + -1D Divide each side by '-19'. t = 5.263157895 + 0.05263157895D Simplifying t = 5.263157895 + 0.05263157895DSolution
t = {0, 5.263157895 + 0.05263157895D}
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