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Simplifying 30 = -7t2 + 12t + 25 Reorder the terms: 30 = 25 + 12t + -7t2 Solving 30 = 25 + 12t + -7t2 Solving for variable 't'. Combine like terms: 30 + -25 = 5 5 + -12t + 7t2 = 25 + 12t + -7t2 + -25 + -12t + 7t2 Reorder the terms: 5 + -12t + 7t2 = 25 + -25 + 12t + -12t + -7t2 + 7t2 Combine like terms: 25 + -25 = 0 5 + -12t + 7t2 = 0 + 12t + -12t + -7t2 + 7t2 5 + -12t + 7t2 = 12t + -12t + -7t2 + 7t2 Combine like terms: 12t + -12t = 0 5 + -12t + 7t2 = 0 + -7t2 + 7t2 5 + -12t + 7t2 = -7t2 + 7t2 Combine like terms: -7t2 + 7t2 = 0 5 + -12t + 7t2 = 0 Factor a trinomial. (5 + -7t)(1 + -1t) = 0Subproblem 1
Set the factor '(5 + -7t)' equal to zero and attempt to solve: Simplifying 5 + -7t = 0 Solving 5 + -7t = 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 + -7t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7t = 0 + -5 -7t = 0 + -5 Combine like terms: 0 + -5 = -5 -7t = -5 Divide each side by '-7'. t = 0.7142857143 Simplifying t = 0.7142857143Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {0.7142857143, 1}
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