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Simplifying 420 = 100t + -5t2 Solving 420 = 100t + -5t2 Solving for variable 't'. Reorder the terms: 420 + -100t + 5t2 = 100t + -100t + -5t2 + 5t2 Combine like terms: 100t + -100t = 0 420 + -100t + 5t2 = 0 + -5t2 + 5t2 420 + -100t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 420 + -100t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(84 + -20t + t2) = 0 Factor a trinomial. 5((6 + -1t)(14 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Subproblem 2
Set the factor '(14 + -1t)' equal to zero and attempt to solve: Simplifying 14 + -1t = 0 Solving 14 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1t = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1t = 0 + -14 -1t = 0 + -14 Combine like terms: 0 + -14 = -14 -1t = -14 Divide each side by '-1'. t = 14 Simplifying t = 14Solution
t = {6, 14}
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