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Simplifying 0.2t2 = -0.17t + 0.03 Reorder the terms: 0.2t2 = 0.03 + -0.17t Solving 0.2t2 = 0.03 + -0.17t Solving for variable 't'. Reorder the terms: -0.03 + 0.17t + 0.2t2 = 0.03 + -0.17t + -0.03 + 0.17t Reorder the terms: -0.03 + 0.17t + 0.2t2 = 0.03 + -0.03 + -0.17t + 0.17t Combine like terms: 0.03 + -0.03 = 0.00 -0.03 + 0.17t + 0.2t2 = 0.00 + -0.17t + 0.17t -0.03 + 0.17t + 0.2t2 = -0.17t + 0.17t Combine like terms: -0.17t + 0.17t = 0.00 -0.03 + 0.17t + 0.2t2 = 0.00 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -0.15 + 0.85t + t2 = 0.0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + 0.85t + 0.15 + t2 = 0.0 + 0.15 Reorder the terms: -0.15 + 0.15 + 0.85t + t2 = 0.0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + 0.85t + t2 = 0.0 + 0.15 0.85t + t2 = 0.0 + 0.15 Combine like terms: 0.0 + 0.15 = 0.15 0.85t + t2 = 0.15 The t term is 0.85t. Take half its coefficient (0.425). Square it (0.180625) and add it to both sides. Add '0.180625' to each side of the equation. 0.85t + 0.180625 + t2 = 0.15 + 0.180625 Reorder the terms: 0.180625 + 0.85t + t2 = 0.15 + 0.180625 Combine like terms: 0.15 + 0.180625 = 0.330625 0.180625 + 0.85t + t2 = 0.330625 Factor a perfect square on the left side: (t + 0.425)(t + 0.425) = 0.330625 Calculate the square root of the right side: 0.575 Break this problem into two subproblems by setting (t + 0.425) equal to 0.575 and -0.575.Subproblem 1
t + 0.425 = 0.575 Simplifying t + 0.425 = 0.575 Reorder the terms: 0.425 + t = 0.575 Solving 0.425 + t = 0.575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.425' to each side of the equation. 0.425 + -0.425 + t = 0.575 + -0.425 Combine like terms: 0.425 + -0.425 = 0.000 0.000 + t = 0.575 + -0.425 t = 0.575 + -0.425 Combine like terms: 0.575 + -0.425 = 0.15 t = 0.15 Simplifying t = 0.15Subproblem 2
t + 0.425 = -0.575 Simplifying t + 0.425 = -0.575 Reorder the terms: 0.425 + t = -0.575 Solving 0.425 + t = -0.575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.425' to each side of the equation. 0.425 + -0.425 + t = -0.575 + -0.425 Combine like terms: 0.425 + -0.425 = 0.000 0.000 + t = -0.575 + -0.425 t = -0.575 + -0.425 Combine like terms: -0.575 + -0.425 = -1 t = -1 Simplifying t = -1Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.15, -1}
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