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Simplifying 2t2 + -2t = 55 Reorder the terms: -2t + 2t2 = 55 Solving -2t + 2t2 = 55 Solving for variable 't'. Reorder the terms: -55 + -2t + 2t2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -2t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27.5 + -1t + t2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + -1t + 27.5 + t2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + -1t + t2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + -1t + t2 = 0 + 27.5 -1t + t2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 -1t + t2 = 27.5 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 27.5 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 27.5 + 0.25 Combine like terms: 27.5 + 0.25 = 27.75 0.25 + -1t + t2 = 27.75 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 27.75 Calculate the square root of the right side: 5.267826876 Break this problem into two subproblems by setting (t + -0.5) equal to 5.267826876 and -5.267826876.Subproblem 1
t + -0.5 = 5.267826876 Simplifying t + -0.5 = 5.267826876 Reorder the terms: -0.5 + t = 5.267826876 Solving -0.5 + t = 5.267826876 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 5.267826876 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 5.267826876 + 0.5 t = 5.267826876 + 0.5 Combine like terms: 5.267826876 + 0.5 = 5.767826876 t = 5.767826876 Simplifying t = 5.767826876Subproblem 2
t + -0.5 = -5.267826876 Simplifying t + -0.5 = -5.267826876 Reorder the terms: -0.5 + t = -5.267826876 Solving -0.5 + t = -5.267826876 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -5.267826876 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -5.267826876 + 0.5 t = -5.267826876 + 0.5 Combine like terms: -5.267826876 + 0.5 = -4.767826876 t = -4.767826876 Simplifying t = -4.767826876Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.767826876, -4.767826876}
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