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Simplifying t2 + -4t = 30 + 3t Reorder the terms: -4t + t2 = 30 + 3t Solving -4t + t2 = 30 + 3t Solving for variable 't'. Reorder the terms: -30 + -4t + -3t + t2 = 30 + 3t + -30 + -3t Combine like terms: -4t + -3t = -7t -30 + -7t + t2 = 30 + 3t + -30 + -3t Reorder the terms: -30 + -7t + t2 = 30 + -30 + 3t + -3t Combine like terms: 30 + -30 = 0 -30 + -7t + t2 = 0 + 3t + -3t -30 + -7t + t2 = 3t + -3t Combine like terms: 3t + -3t = 0 -30 + -7t + t2 = 0 Factor a trinomial. (-3 + -1t)(10 + -1t) = 0Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve: Simplifying -3 + -1t = 0 Solving -3 + -1t = 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 + -1t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t = 0 + 3 -1t = 0 + 3 Combine like terms: 0 + 3 = 3 -1t = 3 Divide each side by '-1'. t = -3 Simplifying t = -3Subproblem 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 = {-3, 10}
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