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Simplifying 36 = -16t2 + 4t + 48 Reorder the terms: 36 = 48 + 4t + -16t2 Solving 36 = 48 + 4t + -16t2 Solving for variable 't'. Combine like terms: 36 + -48 = -12 -12 + -4t + 16t2 = 48 + 4t + -16t2 + -48 + -4t + 16t2 Reorder the terms: -12 + -4t + 16t2 = 48 + -48 + 4t + -4t + -16t2 + 16t2 Combine like terms: 48 + -48 = 0 -12 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2 -12 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 -12 + -4t + 16t2 = 0 + -16t2 + 16t2 -12 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -12 + -4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -1t + 4t2) = 0 Factor a trinomial. 4((-3 + -4t)(1 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {-0.75, 1}
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