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Simplifying 0 = 16t2 + 128t + 87 Reorder the terms: 0 = 87 + 128t + 16t2 Solving 0 = 87 + 128t + 16t2 Solving for variable 't'. Combine like terms: 0 + -87 = -87 -87 + -128t + -16t2 = 87 + 128t + 16t2 + -87 + -128t + -16t2 Reorder the terms: -87 + -128t + -16t2 = 87 + -87 + 128t + -128t + 16t2 + -16t2 Combine like terms: 87 + -87 = 0 -87 + -128t + -16t2 = 0 + 128t + -128t + 16t2 + -16t2 -87 + -128t + -16t2 = 128t + -128t + 16t2 + -16t2 Combine like terms: 128t + -128t = 0 -87 + -128t + -16t2 = 0 + 16t2 + -16t2 -87 + -128t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -87 + -128t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(87 + 128t + 16t2) = 0 Factor a trinomial. -1((29 + 4t)(3 + 4t)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(29 + 4t)' equal to zero and attempt to solve: Simplifying 29 + 4t = 0 Solving 29 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 4t = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 4t = 0 + -29 4t = 0 + -29 Combine like terms: 0 + -29 = -29 4t = -29 Divide each side by '4'. t = -7.25 Simplifying t = -7.25Subproblem 2
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 = -0.75Solution
t = {-7.25, -0.75}
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