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Simplifying 7 + -5t(4t + -1) + -1t = 0 Reorder the terms: 7 + -5t(-1 + 4t) + -1t = 0 7 + (-1 * -5t + 4t * -5t) + -1t = 0 7 + (5t + -20t2) + -1t = 0 Reorder the terms: 7 + 5t + -1t + -20t2 = 0 Combine like terms: 5t + -1t = 4t 7 + 4t + -20t2 = 0 Solving 7 + 4t + -20t2 = 0 Solving for variable 't'. Factor a trinomial. (7 + -10t)(1 + 2t) = 0Subproblem 1
Set the factor '(7 + -10t)' equal to zero and attempt to solve: Simplifying 7 + -10t = 0 Solving 7 + -10t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -10t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10t = 0 + -7 -10t = 0 + -7 Combine like terms: 0 + -7 = -7 -10t = -7 Divide each side by '-10'. t = 0.7 Simplifying t = 0.7Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve: Simplifying 1 + 2t = 0 Solving 1 + 2t = 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 + 2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2t = 0 + -1 2t = 0 + -1 Combine like terms: 0 + -1 = -1 2t = -1 Divide each side by '2'. t = -0.5 Simplifying t = -0.5Solution
t = {0.7, -0.5}
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