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Simplifying t2 + -2t = 40 + 4t Reorder the terms: -2t + t2 = 40 + 4t Solving -2t + t2 = 40 + 4t Solving for variable 't'. Reorder the terms: -40 + -2t + -4t + t2 = 40 + 4t + -40 + -4t Combine like terms: -2t + -4t = -6t -40 + -6t + t2 = 40 + 4t + -40 + -4t Reorder the terms: -40 + -6t + t2 = 40 + -40 + 4t + -4t Combine like terms: 40 + -40 = 0 -40 + -6t + t2 = 0 + 4t + -4t -40 + -6t + t2 = 4t + -4t Combine like terms: 4t + -4t = 0 -40 + -6t + t2 = 0 Factor a trinomial. (-4 + -1t)(10 + -1t) = 0Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve: Simplifying -4 + -1t = 0 Solving -4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1t = 0 + 4 -1t = 0 + 4 Combine like terms: 0 + 4 = 4 -1t = 4 Divide each side by '-1'. t = -4 Simplifying t = -4Subproblem 2
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {-4, 10}
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