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Simplifying 100 = -16t2 + -20t + 436 Reorder the terms: 100 = 436 + -20t + -16t2 Solving 100 = 436 + -20t + -16t2 Solving for variable 't'. Combine like terms: 100 + -436 = -336 -336 + 20t + 16t2 = 436 + -20t + -16t2 + -436 + 20t + 16t2 Reorder the terms: -336 + 20t + 16t2 = 436 + -436 + -20t + 20t + -16t2 + 16t2 Combine like terms: 436 + -436 = 0 -336 + 20t + 16t2 = 0 + -20t + 20t + -16t2 + 16t2 -336 + 20t + 16t2 = -20t + 20t + -16t2 + 16t2 Combine like terms: -20t + 20t = 0 -336 + 20t + 16t2 = 0 + -16t2 + 16t2 -336 + 20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -336 + 20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-84 + 5t + 4t2) = 0 Factor a trinomial. 4((-21 + -4t)(4 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + -4t)' equal to zero and attempt to solve: Simplifying -21 + -4t = 0 Solving -21 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -4t = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -4t = 0 + 21 -4t = 0 + 21 Combine like terms: 0 + 21 = 21 -4t = 21 Divide each side by '-4'. t = -5.25 Simplifying t = -5.25Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-5.25, 4}
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