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Simplifying 5t2 = 31t + 28 Reorder the terms: 5t2 = 28 + 31t Solving 5t2 = 28 + 31t Solving for variable 't'. Reorder the terms: -28 + -31t + 5t2 = 28 + 31t + -28 + -31t Reorder the terms: -28 + -31t + 5t2 = 28 + -28 + 31t + -31t Combine like terms: 28 + -28 = 0 -28 + -31t + 5t2 = 0 + 31t + -31t -28 + -31t + 5t2 = 31t + -31t Combine like terms: 31t + -31t = 0 -28 + -31t + 5t2 = 0 Factor a trinomial. (-4 + -5t)(7 + -1t) = 0Subproblem 1
Set the factor '(-4 + -5t)' equal to zero and attempt to solve: Simplifying -4 + -5t = 0 Solving -4 + -5t = 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 + -5t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5t = 0 + 4 -5t = 0 + 4 Combine like terms: 0 + 4 = 4 -5t = 4 Divide each side by '-5'. t = -0.8 Simplifying t = -0.8Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 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 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-0.8, 7}
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