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Simplifying 84 = -16t2 + 100t + 84 Reorder the terms: 84 = 84 + 100t + -16t2 Add '-84' to each side of the equation. 84 + -84 = 84 + 100t + -84 + -16t2 Combine like terms: 84 + -84 = 0 0 = 84 + 100t + -84 + -16t2 Reorder the terms: 0 = 84 + -84 + 100t + -16t2 Combine like terms: 84 + -84 = 0 0 = 0 + 100t + -16t2 0 = 100t + -16t2 Solving 0 = 100t + -16t2 Solving for variable 't'. Remove the zero: -100t + 16t2 = 100t + -16t2 + -100t + 16t2 Reorder the terms: -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 -100t + 16t2 = 0 + -16t2 + 16t2 -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(-25 + 4t) = 0 Ignore the factor 4.Subproblem 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 '(-25 + 4t)' equal to zero and attempt to solve: Simplifying -25 + 4t = 0 Solving -25 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 4t = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4t = 0 + 25 4t = 0 + 25 Combine like terms: 0 + 25 = 25 4t = 25 Divide each side by '4'. t = 6.25 Simplifying t = 6.25Solution
t = {0, 6.25}
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