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Simplifying 19.8912t2 + -142.704t + 124.48 = 0 Reorder the terms: 124.48 + -142.704t + 19.8912t2 = 0 Solving 124.48 + -142.704t + 19.8912t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 19.8912 the coefficient of the squared term: Divide each side by '19.8912'. 6.258043758 + -7.174227799t + t2 = 0 Move the constant term to the right: Add '-6.258043758' to each side of the equation. 6.258043758 + -7.174227799t + -6.258043758 + t2 = 0 + -6.258043758 Reorder the terms: 6.258043758 + -6.258043758 + -7.174227799t + t2 = 0 + -6.258043758 Combine like terms: 6.258043758 + -6.258043758 = 0.000000000 0.000000000 + -7.174227799t + t2 = 0 + -6.258043758 -7.174227799t + t2 = 0 + -6.258043758 Combine like terms: 0 + -6.258043758 = -6.258043758 -7.174227799t + t2 = -6.258043758 The t term is -7.174227799t. Take half its coefficient (-3.5871139). Square it (12.86738613) and add it to both sides. Add '12.86738613' to each side of the equation. -7.174227799t + 12.86738613 + t2 = -6.258043758 + 12.86738613 Reorder the terms: 12.86738613 + -7.174227799t + t2 = -6.258043758 + 12.86738613 Combine like terms: -6.258043758 + 12.86738613 = 6.609342372 12.86738613 + -7.174227799t + t2 = 6.609342372 Factor a perfect square on the left side: (t + -3.5871139)(t + -3.5871139) = 6.609342372 Calculate the square root of the right side: 2.570864129 Break this problem into two subproblems by setting (t + -3.5871139) equal to 2.570864129 and -2.570864129.Subproblem 1
t + -3.5871139 = 2.570864129 Simplifying t + -3.5871139 = 2.570864129 Reorder the terms: -3.5871139 + t = 2.570864129 Solving -3.5871139 + t = 2.570864129 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5871139' to each side of the equation. -3.5871139 + 3.5871139 + t = 2.570864129 + 3.5871139 Combine like terms: -3.5871139 + 3.5871139 = 0.0000000 0.0000000 + t = 2.570864129 + 3.5871139 t = 2.570864129 + 3.5871139 Combine like terms: 2.570864129 + 3.5871139 = 6.157978029 t = 6.157978029 Simplifying t = 6.157978029Subproblem 2
t + -3.5871139 = -2.570864129 Simplifying t + -3.5871139 = -2.570864129 Reorder the terms: -3.5871139 + t = -2.570864129 Solving -3.5871139 + t = -2.570864129 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5871139' to each side of the equation. -3.5871139 + 3.5871139 + t = -2.570864129 + 3.5871139 Combine like terms: -3.5871139 + 3.5871139 = 0.0000000 0.0000000 + t = -2.570864129 + 3.5871139 t = -2.570864129 + 3.5871139 Combine like terms: -2.570864129 + 3.5871139 = 1.016249771 t = 1.016249771 Simplifying t = 1.016249771Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.157978029, 1.016249771}
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