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Simplifying 0 = -16t2 + 156t + 40 Reorder the terms: 0 = 40 + 156t + -16t2 Solving 0 = 40 + 156t + -16t2 Solving for variable 't'. Combine like terms: 0 + -40 = -40 -40 + -156t + 16t2 = 40 + 156t + -16t2 + -40 + -156t + 16t2 Reorder the terms: -40 + -156t + 16t2 = 40 + -40 + 156t + -156t + -16t2 + 16t2 Combine like terms: 40 + -40 = 0 -40 + -156t + 16t2 = 0 + 156t + -156t + -16t2 + 16t2 -40 + -156t + 16t2 = 156t + -156t + -16t2 + 16t2 Combine like terms: 156t + -156t = 0 -40 + -156t + 16t2 = 0 + -16t2 + 16t2 -40 + -156t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -40 + -156t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -39t + 4t2) = 0 Factor a trinomial. 4((-1 + -4t)(10 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -4t)' equal to zero and attempt to solve: Simplifying -1 + -4t = 0 Solving -1 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4t = 0 + 1 -4t = 0 + 1 Combine like terms: 0 + 1 = 1 -4t = 1 Divide each side by '-4'. t = -0.25 Simplifying t = -0.25Subproblem 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 = {-0.25, 10}
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