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Simplifying 0 = -16t2 + 150t + 100 Reorder the terms: 0 = 100 + 150t + -16t2 Solving 0 = 100 + 150t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -150t + 16t2 = 100 + 150t + -16t2 + -100 + -150t + 16t2 Reorder the terms: -100 + -150t + 16t2 = 100 + -100 + 150t + -150t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -100 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -100 + -150t + 16t2 = 0 + -16t2 + 16t2 -100 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -150t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -75t + 8t2) = 0 Factor a trinomial. 2((-5 + -8t)(10 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -8t)' equal to zero and attempt to solve: Simplifying -5 + -8t = 0 Solving -5 + -8t = 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 + -8t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8t = 0 + 5 -8t = 0 + 5 Combine like terms: 0 + 5 = 5 -8t = 5 Divide each side by '-8'. t = -0.625 Simplifying t = -0.625Subproblem 2
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {-0.625, 10}
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