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Simplifying 20.1276t2 + -124.512t + 124.06 = 0 Reorder the terms: 124.06 + -124.512t + 20.1276t2 = 0 Solving 124.06 + -124.512t + 20.1276t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 20.1276 the coefficient of the squared term: Divide each side by '20.1276'. 6.163675749 + -6.186132475t + t2 = 0 Move the constant term to the right: Add '-6.163675749' to each side of the equation. 6.163675749 + -6.186132475t + -6.163675749 + t2 = 0 + -6.163675749 Reorder the terms: 6.163675749 + -6.163675749 + -6.186132475t + t2 = 0 + -6.163675749 Combine like terms: 6.163675749 + -6.163675749 = 0.000000000 0.000000000 + -6.186132475t + t2 = 0 + -6.163675749 -6.186132475t + t2 = 0 + -6.163675749 Combine like terms: 0 + -6.163675749 = -6.163675749 -6.186132475t + t2 = -6.163675749 The t term is -6.186132475t. Take half its coefficient (-3.093066238). Square it (9.567058753) and add it to both sides. Add '9.567058753' to each side of the equation. -6.186132475t + 9.567058753 + t2 = -6.163675749 + 9.567058753 Reorder the terms: 9.567058753 + -6.186132475t + t2 = -6.163675749 + 9.567058753 Combine like terms: -6.163675749 + 9.567058753 = 3.403383004 9.567058753 + -6.186132475t + t2 = 3.403383004 Factor a perfect square on the left side: (t + -3.093066238)(t + -3.093066238) = 3.403383004 Calculate the square root of the right side: 1.844826009 Break this problem into two subproblems by setting (t + -3.093066238) equal to 1.844826009 and -1.844826009.Subproblem 1
t + -3.093066238 = 1.844826009 Simplifying t + -3.093066238 = 1.844826009 Reorder the terms: -3.093066238 + t = 1.844826009 Solving -3.093066238 + t = 1.844826009 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.093066238' to each side of the equation. -3.093066238 + 3.093066238 + t = 1.844826009 + 3.093066238 Combine like terms: -3.093066238 + 3.093066238 = 0.000000000 0.000000000 + t = 1.844826009 + 3.093066238 t = 1.844826009 + 3.093066238 Combine like terms: 1.844826009 + 3.093066238 = 4.937892247 t = 4.937892247 Simplifying t = 4.937892247Subproblem 2
t + -3.093066238 = -1.844826009 Simplifying t + -3.093066238 = -1.844826009 Reorder the terms: -3.093066238 + t = -1.844826009 Solving -3.093066238 + t = -1.844826009 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.093066238' to each side of the equation. -3.093066238 + 3.093066238 + t = -1.844826009 + 3.093066238 Combine like terms: -3.093066238 + 3.093066238 = 0.000000000 0.000000000 + t = -1.844826009 + 3.093066238 t = -1.844826009 + 3.093066238 Combine like terms: -1.844826009 + 3.093066238 = 1.248240229 t = 1.248240229 Simplifying t = 1.248240229Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.937892247, 1.248240229}
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