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Simplifying 300 = 40t + 4t2 Solving 300 = 40t + 4t2 Solving for variable 't'. Reorder the terms: 300 + -40t + -4t2 = 40t + -40t + 4t2 + -4t2 Combine like terms: 40t + -40t = 0 300 + -40t + -4t2 = 0 + 4t2 + -4t2 300 + -40t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 300 + -40t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(75 + -10t + -1t2) = 0 Factor a trinomial. 4((5 + -1t)(15 + t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Subproblem 2
Set the factor '(15 + t)' equal to zero and attempt to solve: Simplifying 15 + t = 0 Solving 15 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + t = 0 + -15 t = 0 + -15 Combine like terms: 0 + -15 = -15 t = -15 Simplifying t = -15Solution
t = {5, -15}
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