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Simplifying 4t2 + 80t + 20 = -184 Reorder the terms: 20 + 80t + 4t2 = -184 Solving 20 + 80t + 4t2 = -184 Solving for variable 't'. Reorder the terms: 20 + 184 + 80t + 4t2 = -184 + 184 Combine like terms: 20 + 184 = 204 204 + 80t + 4t2 = -184 + 184 Combine like terms: -184 + 184 = 0 204 + 80t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(51 + 20t + t2) = 0 Factor a trinomial. 4((17 + t)(3 + t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(17 + t)' equal to zero and attempt to solve: Simplifying 17 + t = 0 Solving 17 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + t = 0 + -17 Combine like terms: 17 + -17 = 0 0 + t = 0 + -17 t = 0 + -17 Combine like terms: 0 + -17 = -17 t = -17 Simplifying t = -17Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Solution
t = {-17, -3}
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