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Simplifying 400 = 70t + -3t2 Solving 400 = 70t + -3t2 Solving for variable 't'. Reorder the terms: 400 + -70t + 3t2 = 70t + -70t + -3t2 + 3t2 Combine like terms: 70t + -70t = 0 400 + -70t + 3t2 = 0 + -3t2 + 3t2 400 + -70t + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 400 + -70t + 3t2 = 0 Factor a trinomial. (10 + -1t)(40 + -3t) = 0Subproblem 1
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 = 10Subproblem 2
Set the factor '(40 + -3t)' equal to zero and attempt to solve: Simplifying 40 + -3t = 0 Solving 40 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -3t = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -3t = 0 + -40 -3t = 0 + -40 Combine like terms: 0 + -40 = -40 -3t = -40 Divide each side by '-3'. t = 13.33333333 Simplifying t = 13.33333333Solution
t = {10, 13.33333333}
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