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Simplifying 0 = 16t2 + 100t + 100 Reorder the terms: 0 = 100 + 100t + 16t2 Solving 0 = 100 + 100t + 16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -100t + -16t2 = 100 + 100t + 16t2 + -100 + -100t + -16t2 Reorder the terms: -100 + -100t + -16t2 = 100 + -100 + 100t + -100t + 16t2 + -16t2 Combine like terms: 100 + -100 = 0 -100 + -100t + -16t2 = 0 + 100t + -100t + 16t2 + -16t2 -100 + -100t + -16t2 = 100t + -100t + 16t2 + -16t2 Combine like terms: 100t + -100t = 0 -100 + -100t + -16t2 = 0 + 16t2 + -16t2 -100 + -100t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -100 + -100t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(25 + 25t + 4t2) = 0 Factor a trinomial. -4((5 + t)(5 + 4t)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 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 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Subproblem 2
Set the factor '(5 + 4t)' equal to zero and attempt to solve: Simplifying 5 + 4t = 0 Solving 5 + 4t = 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 + 4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4t = 0 + -5 4t = 0 + -5 Combine like terms: 0 + -5 = -5 4t = -5 Divide each side by '4'. t = -1.25 Simplifying t = -1.25Solution
t = {-5, -1.25}
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