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Simplifying 156 = -16t2 + 100t + 20 Reorder the terms: 156 = 20 + 100t + -16t2 Solving 156 = 20 + 100t + -16t2 Solving for variable 't'. Combine like terms: 156 + -20 = 136 136 + -100t + 16t2 = 20 + 100t + -16t2 + -20 + -100t + 16t2 Reorder the terms: 136 + -100t + 16t2 = 20 + -20 + 100t + -100t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 136 + -100t + 16t2 = 0 + 100t + -100t + -16t2 + 16t2 136 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 136 + -100t + 16t2 = 0 + -16t2 + 16t2 136 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 136 + -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(34 + -25t + 4t2) = 0 Factor a trinomial. 4((2 + -1t)(17 + -4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(17 + -4t)' equal to zero and attempt to solve: Simplifying 17 + -4t = 0 Solving 17 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -4t = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -4t = 0 + -17 -4t = 0 + -17 Combine like terms: 0 + -17 = -17 -4t = -17 Divide each side by '-4'. t = 4.25 Simplifying t = 4.25Solution
t = {2, 4.25}
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