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Simplifying 20t + -2t2 = 32 Solving 20t + -2t2 = 32 Solving for variable 't'. Reorder the terms: -32 + 20t + -2t2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 20t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 10t + -1t2) = 0 Factor a trinomial. 2((-8 + t)(2 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + t)' equal to zero and attempt to solve: Simplifying -8 + t = 0 Solving -8 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + t = 0 + 8 t = 0 + 8 Combine like terms: 0 + 8 = 8 t = 8 Simplifying t = 8Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {8, 2}
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