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Simplifying -13t + -40 = t2 Reorder the terms: -40 + -13t = t2 Solving -40 + -13t = t2 Solving for variable 't'. Combine like terms: t2 + -1t2 = 0 -40 + -13t + -1t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 13t + t2) = 0 Factor a trinomial. -1((8 + t)(5 + t)) = 0 Ignore the factor -1.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 '(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 = {-8, -5}
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