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Simplifying 0 = 2t2 + 20t + 50 Reorder the terms: 0 = 50 + 20t + 2t2 Solving 0 = 50 + 20t + 2t2 Solving for variable 't'. Combine like terms: 0 + -50 = -50 -50 + -20t + -2t2 = 50 + 20t + 2t2 + -50 + -20t + -2t2 Reorder the terms: -50 + -20t + -2t2 = 50 + -50 + 20t + -20t + 2t2 + -2t2 Combine like terms: 50 + -50 = 0 -50 + -20t + -2t2 = 0 + 20t + -20t + 2t2 + -2t2 -50 + -20t + -2t2 = 20t + -20t + 2t2 + -2t2 Combine like terms: 20t + -20t = 0 -50 + -20t + -2t2 = 0 + 2t2 + -2t2 -50 + -20t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -50 + -20t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(25 + 10t + t2) = 0 Factor a trinomial. -2((5 + t)(5 + t)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Subproblem 2
Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Solution
t = {-5, -5}
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