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Simplifying 1.15t2 + -40.56t = 40.56 Reorder the terms: -40.56t + 1.15t2 = 40.56 Solving -40.56t + 1.15t2 = 40.56 Solving for variable 't'. Reorder the terms: -40.56 + -40.56t + 1.15t2 = 40.56 + -40.56 Combine like terms: 40.56 + -40.56 = 0.00 -40.56 + -40.56t + 1.15t2 = 0.00 Begin completing the square. Divide all terms by 1.15 the coefficient of the squared term: Divide each side by '1.15'. -35.26956522 + -35.26956522t + t2 = 0 Move the constant term to the right: Add '35.26956522' to each side of the equation. -35.26956522 + -35.26956522t + 35.26956522 + t2 = 0 + 35.26956522 Reorder the terms: -35.26956522 + 35.26956522 + -35.26956522t + t2 = 0 + 35.26956522 Combine like terms: -35.26956522 + 35.26956522 = 0.00000000 0.00000000 + -35.26956522t + t2 = 0 + 35.26956522 -35.26956522t + t2 = 0 + 35.26956522 Combine like terms: 0 + 35.26956522 = 35.26956522 -35.26956522t + t2 = 35.26956522 The t term is -35.26956522t. Take half its coefficient (-17.63478261). Square it (310.9855577) and add it to both sides. Add '310.9855577' to each side of the equation. -35.26956522t + 310.9855577 + t2 = 35.26956522 + 310.9855577 Reorder the terms: 310.9855577 + -35.26956522t + t2 = 35.26956522 + 310.9855577 Combine like terms: 35.26956522 + 310.9855577 = 346.25512292 310.9855577 + -35.26956522t + t2 = 346.25512292 Factor a perfect square on the left side: (t + -17.63478261)(t + -17.63478261) = 346.25512292 Calculate the square root of the right side: 18.607931721 Break this problem into two subproblems by setting (t + -17.63478261) equal to 18.607931721 and -18.607931721.Subproblem 1
t + -17.63478261 = 18.607931721 Simplifying t + -17.63478261 = 18.607931721 Reorder the terms: -17.63478261 + t = 18.607931721 Solving -17.63478261 + t = 18.607931721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17.63478261' to each side of the equation. -17.63478261 + 17.63478261 + t = 18.607931721 + 17.63478261 Combine like terms: -17.63478261 + 17.63478261 = 0.00000000 0.00000000 + t = 18.607931721 + 17.63478261 t = 18.607931721 + 17.63478261 Combine like terms: 18.607931721 + 17.63478261 = 36.242714331 t = 36.242714331 Simplifying t = 36.242714331Subproblem 2
t + -17.63478261 = -18.607931721 Simplifying t + -17.63478261 = -18.607931721 Reorder the terms: -17.63478261 + t = -18.607931721 Solving -17.63478261 + t = -18.607931721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17.63478261' to each side of the equation. -17.63478261 + 17.63478261 + t = -18.607931721 + 17.63478261 Combine like terms: -17.63478261 + 17.63478261 = 0.00000000 0.00000000 + t = -18.607931721 + 17.63478261 t = -18.607931721 + 17.63478261 Combine like terms: -18.607931721 + 17.63478261 = -0.973149111 t = -0.973149111 Simplifying t = -0.973149111Solution
The solution to the problem is based on the solutions from the subproblems. t = {36.242714331, -0.973149111}
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