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Simplifying 200 = 68t + -4.9t2 Solving 200 = 68t + -4.9t2 Solving for variable 't'. Reorder the terms: 200 + -68t + 4.9t2 = 68t + -68t + -4.9t2 + 4.9t2 Combine like terms: 68t + -68t = 0 200 + -68t + 4.9t2 = 0 + -4.9t2 + 4.9t2 200 + -68t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 200 + -68t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 40.81632653 + -13.87755102t + t2 = 0 Move the constant term to the right: Add '-40.81632653' to each side of the equation. 40.81632653 + -13.87755102t + -40.81632653 + t2 = 0 + -40.81632653 Reorder the terms: 40.81632653 + -40.81632653 + -13.87755102t + t2 = 0 + -40.81632653 Combine like terms: 40.81632653 + -40.81632653 = 0.00000000 0.00000000 + -13.87755102t + t2 = 0 + -40.81632653 -13.87755102t + t2 = 0 + -40.81632653 Combine like terms: 0 + -40.81632653 = -40.81632653 -13.87755102t + t2 = -40.81632653 The t term is -13.87755102t. Take half its coefficient (-6.93877551). Square it (48.14660558) and add it to both sides. Add '48.14660558' to each side of the equation. -13.87755102t + 48.14660558 + t2 = -40.81632653 + 48.14660558 Reorder the terms: 48.14660558 + -13.87755102t + t2 = -40.81632653 + 48.14660558 Combine like terms: -40.81632653 + 48.14660558 = 7.33027905 48.14660558 + -13.87755102t + t2 = 7.33027905 Factor a perfect square on the left side: (t + -6.93877551)(t + -6.93877551) = 7.33027905 Calculate the square root of the right side: 2.707448808 Break this problem into two subproblems by setting (t + -6.93877551) equal to 2.707448808 and -2.707448808.Subproblem 1
t + -6.93877551 = 2.707448808 Simplifying t + -6.93877551 = 2.707448808 Reorder the terms: -6.93877551 + t = 2.707448808 Solving -6.93877551 + t = 2.707448808 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.93877551' to each side of the equation. -6.93877551 + 6.93877551 + t = 2.707448808 + 6.93877551 Combine like terms: -6.93877551 + 6.93877551 = 0.00000000 0.00000000 + t = 2.707448808 + 6.93877551 t = 2.707448808 + 6.93877551 Combine like terms: 2.707448808 + 6.93877551 = 9.646224318 t = 9.646224318 Simplifying t = 9.646224318Subproblem 2
t + -6.93877551 = -2.707448808 Simplifying t + -6.93877551 = -2.707448808 Reorder the terms: -6.93877551 + t = -2.707448808 Solving -6.93877551 + t = -2.707448808 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.93877551' to each side of the equation. -6.93877551 + 6.93877551 + t = -2.707448808 + 6.93877551 Combine like terms: -6.93877551 + 6.93877551 = 0.00000000 0.00000000 + t = -2.707448808 + 6.93877551 t = -2.707448808 + 6.93877551 Combine like terms: -2.707448808 + 6.93877551 = 4.231326702 t = 4.231326702 Simplifying t = 4.231326702Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.646224318, 4.231326702}
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