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Simplifying 187 = 2.8t + 0.5(-0.0209625668) * t2 Multiply 0.5 * -0.0209625668 187 = 2.8t + -0.0104812834t2 Solving 187 = 2.8t + -0.0104812834t2 Solving for variable 't'. Reorder the terms: 187 + -2.8t + 0.0104812834t2 = 2.8t + -2.8t + -0.0104812834t2 + 0.0104812834t2 Combine like terms: 2.8t + -2.8t = 0.0 187 + -2.8t + 0.0104812834t2 = 0.0 + -0.0104812834t2 + 0.0104812834t2 187 + -2.8t + 0.0104812834t2 = -0.0104812834t2 + 0.0104812834t2 Combine like terms: -0.0104812834t2 + 0.0104812834t2 = 0.0000000000 187 + -2.8t + 0.0104812834t2 = 0.0000000000 Begin completing the square. Divide all terms by 0.0104812834 the coefficient of the squared term: Divide each side by '0.0104812834'. 17841.32657 + -267.1428577t + t2 = 0 Move the constant term to the right: Add '-17841.32657' to each side of the equation. 17841.32657 + -267.1428577t + -17841.32657 + t2 = 0 + -17841.32657 Reorder the terms: 17841.32657 + -17841.32657 + -267.1428577t + t2 = 0 + -17841.32657 Combine like terms: 17841.32657 + -17841.32657 = 0.00000 0.00000 + -267.1428577t + t2 = 0 + -17841.32657 -267.1428577t + t2 = 0 + -17841.32657 Combine like terms: 0 + -17841.32657 = -17841.32657 -267.1428577t + t2 = -17841.32657 The t term is -267.1428577t. Take half its coefficient (-133.5714289). Square it (17841.32662) and add it to both sides. Add '17841.32662' to each side of the equation. -267.1428577t + 17841.32662 + t2 = -17841.32657 + 17841.32662 Reorder the terms: 17841.32662 + -267.1428577t + t2 = -17841.32657 + 17841.32662 Combine like terms: -17841.32657 + 17841.32662 = 0.00005 17841.32662 + -267.1428577t + t2 = 0.00005 Factor a perfect square on the left side: (t + -133.5714289)(t + -133.5714289) = 0.00005 Calculate the square root of the right side: 0.007071068 Break this problem into two subproblems by setting (t + -133.5714289) equal to 0.007071068 and -0.007071068.Subproblem 1
t + -133.5714289 = 0.007071068 Simplifying t + -133.5714289 = 0.007071068 Reorder the terms: -133.5714289 + t = 0.007071068 Solving -133.5714289 + t = 0.007071068 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '133.5714289' to each side of the equation. -133.5714289 + 133.5714289 + t = 0.007071068 + 133.5714289 Combine like terms: -133.5714289 + 133.5714289 = 0.0000000 0.0000000 + t = 0.007071068 + 133.5714289 t = 0.007071068 + 133.5714289 Combine like terms: 0.007071068 + 133.5714289 = 133.578499968 t = 133.578499968 Simplifying t = 133.578499968Subproblem 2
t + -133.5714289 = -0.007071068 Simplifying t + -133.5714289 = -0.007071068 Reorder the terms: -133.5714289 + t = -0.007071068 Solving -133.5714289 + t = -0.007071068 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '133.5714289' to each side of the equation. -133.5714289 + 133.5714289 + t = -0.007071068 + 133.5714289 Combine like terms: -133.5714289 + 133.5714289 = 0.0000000 0.0000000 + t = -0.007071068 + 133.5714289 t = -0.007071068 + 133.5714289 Combine like terms: -0.007071068 + 133.5714289 = 133.564357832 t = 133.564357832 Simplifying t = 133.564357832Solution
The solution to the problem is based on the solutions from the subproblems. t = {133.578499968, 133.564357832}
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