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Simplifying -32t2 + 128t = r(t) Reorder the terms: 128t + -32t2 = r(t) Multiply r * t 128t + -32t2 = rt Solving 128t + -32t2 = rt Solving for variable 't'. Reorder the terms: -1rt + 128t + -32t2 = rt + -1rt Combine like terms: rt + -1rt = 0 -1rt + 128t + -32t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-1r + 128 + -32t) = 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 '(-1r + 128 + -32t)' equal to zero and attempt to solve: Simplifying -1r + 128 + -32t = 0 Reorder the terms: 128 + -1r + -32t = 0 Solving 128 + -1r + -32t = 0 Move all terms containing t to the left, all other terms to the right. Add '-128' to each side of the equation. 128 + -1r + -128 + -32t = 0 + -128 Reorder the terms: 128 + -128 + -1r + -32t = 0 + -128 Combine like terms: 128 + -128 = 0 0 + -1r + -32t = 0 + -128 -1r + -32t = 0 + -128 Combine like terms: 0 + -128 = -128 -1r + -32t = -128 Add 'r' to each side of the equation. -1r + r + -32t = -128 + r Combine like terms: -1r + r = 0 0 + -32t = -128 + r -32t = -128 + r Divide each side by '-32'. t = 4 + -0.03125r Simplifying t = 4 + -0.03125rSolution
t = {0, 4 + -0.03125r}
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