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Simplifying 0 = -1.85t2 + 20t + 1 Reorder the terms: 0 = 1 + 20t + -1.85t2 Solving 0 = 1 + 20t + -1.85t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -20t + 1.85t2 = 1 + 20t + -1.85t2 + -1 + -20t + 1.85t2 Reorder the terms: -1 + -20t + 1.85t2 = 1 + -1 + 20t + -20t + -1.85t2 + 1.85t2 Combine like terms: 1 + -1 = 0 -1 + -20t + 1.85t2 = 0 + 20t + -20t + -1.85t2 + 1.85t2 -1 + -20t + 1.85t2 = 20t + -20t + -1.85t2 + 1.85t2 Combine like terms: 20t + -20t = 0 -1 + -20t + 1.85t2 = 0 + -1.85t2 + 1.85t2 -1 + -20t + 1.85t2 = -1.85t2 + 1.85t2 Combine like terms: -1.85t2 + 1.85t2 = 0.00 -1 + -20t + 1.85t2 = 0.00 Begin completing the square. Divide all terms by 1.85 the coefficient of the squared term: Divide each side by '1.85'. -0.5405405405 + -10.81081081t + t2 = 0 Move the constant term to the right: Add '0.5405405405' to each side of the equation. -0.5405405405 + -10.81081081t + 0.5405405405 + t2 = 0 + 0.5405405405 Reorder the terms: -0.5405405405 + 0.5405405405 + -10.81081081t + t2 = 0 + 0.5405405405 Combine like terms: -0.5405405405 + 0.5405405405 = 0.0000000000 0.0000000000 + -10.81081081t + t2 = 0 + 0.5405405405 -10.81081081t + t2 = 0 + 0.5405405405 Combine like terms: 0 + 0.5405405405 = 0.5405405405 -10.81081081t + t2 = 0.5405405405 The t term is -10.81081081t. Take half its coefficient (-5.405405405). Square it (29.21840759) and add it to both sides. Add '29.21840759' to each side of the equation. -10.81081081t + 29.21840759 + t2 = 0.5405405405 + 29.21840759 Reorder the terms: 29.21840759 + -10.81081081t + t2 = 0.5405405405 + 29.21840759 Combine like terms: 0.5405405405 + 29.21840759 = 29.7589481305 29.21840759 + -10.81081081t + t2 = 29.7589481305 Factor a perfect square on the left side: (t + -5.405405405)(t + -5.405405405) = 29.7589481305 Calculate the square root of the right side: 5.455176269 Break this problem into two subproblems by setting (t + -5.405405405) equal to 5.455176269 and -5.455176269.Subproblem 1
t + -5.405405405 = 5.455176269 Simplifying t + -5.405405405 = 5.455176269 Reorder the terms: -5.405405405 + t = 5.455176269 Solving -5.405405405 + t = 5.455176269 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.405405405' to each side of the equation. -5.405405405 + 5.405405405 + t = 5.455176269 + 5.405405405 Combine like terms: -5.405405405 + 5.405405405 = 0.000000000 0.000000000 + t = 5.455176269 + 5.405405405 t = 5.455176269 + 5.405405405 Combine like terms: 5.455176269 + 5.405405405 = 10.860581674 t = 10.860581674 Simplifying t = 10.860581674Subproblem 2
t + -5.405405405 = -5.455176269 Simplifying t + -5.405405405 = -5.455176269 Reorder the terms: -5.405405405 + t = -5.455176269 Solving -5.405405405 + t = -5.455176269 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.405405405' to each side of the equation. -5.405405405 + 5.405405405 + t = -5.455176269 + 5.405405405 Combine like terms: -5.405405405 + 5.405405405 = 0.000000000 0.000000000 + t = -5.455176269 + 5.405405405 t = -5.455176269 + 5.405405405 Combine like terms: -5.455176269 + 5.405405405 = -0.049770864 t = -0.049770864 Simplifying t = -0.049770864Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.860581674, -0.049770864}
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