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Simplifying 0 = 4.90t2 + 19t + -2.30 Reorder the terms: 0 = -2.30 + 19t + 4.90t2 Solving 0 = -2.30 + 19t + 4.90t2 Solving for variable 't'. Combine like terms: 0 + 2.30 = 2.3 2.3 + -19t + -4.90t2 = -2.30 + 19t + 4.90t2 + 2.30 + -19t + -4.90t2 Reorder the terms: 2.3 + -19t + -4.90t2 = -2.30 + 2.30 + 19t + -19t + 4.90t2 + -4.90t2 Combine like terms: -2.30 + 2.30 = 0.00 2.3 + -19t + -4.90t2 = 0.00 + 19t + -19t + 4.90t2 + -4.90t2 2.3 + -19t + -4.90t2 = 19t + -19t + 4.90t2 + -4.90t2 Combine like terms: 19t + -19t = 0 2.3 + -19t + -4.90t2 = 0 + 4.90t2 + -4.90t2 2.3 + -19t + -4.90t2 = 4.90t2 + -4.90t2 Combine like terms: 4.90t2 + -4.90t2 = 0.00 2.3 + -19t + -4.90t2 = 0.00 Begin completing the square. Divide all terms by -4.90 the coefficient of the squared term: Divide each side by '-4.90'. -0.4693877551 + 3.87755102t + t2 = 0 Move the constant term to the right: Add '0.4693877551' to each side of the equation. -0.4693877551 + 3.87755102t + 0.4693877551 + t2 = 0 + 0.4693877551 Reorder the terms: -0.4693877551 + 0.4693877551 + 3.87755102t + t2 = 0 + 0.4693877551 Combine like terms: -0.4693877551 + 0.4693877551 = 0.0000000000 0.0000000000 + 3.87755102t + t2 = 0 + 0.4693877551 3.87755102t + t2 = 0 + 0.4693877551 Combine like terms: 0 + 0.4693877551 = 0.4693877551 3.87755102t + t2 = 0.4693877551 The t term is 3.87755102t. Take half its coefficient (1.93877551). Square it (3.758850478) and add it to both sides. Add '3.758850478' to each side of the equation. 3.87755102t + 3.758850478 + t2 = 0.4693877551 + 3.758850478 Reorder the terms: 3.758850478 + 3.87755102t + t2 = 0.4693877551 + 3.758850478 Combine like terms: 0.4693877551 + 3.758850478 = 4.2282382331 3.758850478 + 3.87755102t + t2 = 4.2282382331 Factor a perfect square on the left side: (t + 1.93877551)(t + 1.93877551) = 4.2282382331 Calculate the square root of the right side: 2.056268035 Break this problem into two subproblems by setting (t + 1.93877551) equal to 2.056268035 and -2.056268035.Subproblem 1
t + 1.93877551 = 2.056268035 Simplifying t + 1.93877551 = 2.056268035 Reorder the terms: 1.93877551 + t = 2.056268035 Solving 1.93877551 + t = 2.056268035 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.93877551' to each side of the equation. 1.93877551 + -1.93877551 + t = 2.056268035 + -1.93877551 Combine like terms: 1.93877551 + -1.93877551 = 0.00000000 0.00000000 + t = 2.056268035 + -1.93877551 t = 2.056268035 + -1.93877551 Combine like terms: 2.056268035 + -1.93877551 = 0.117492525 t = 0.117492525 Simplifying t = 0.117492525Subproblem 2
t + 1.93877551 = -2.056268035 Simplifying t + 1.93877551 = -2.056268035 Reorder the terms: 1.93877551 + t = -2.056268035 Solving 1.93877551 + t = -2.056268035 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.93877551' to each side of the equation. 1.93877551 + -1.93877551 + t = -2.056268035 + -1.93877551 Combine like terms: 1.93877551 + -1.93877551 = 0.00000000 0.00000000 + t = -2.056268035 + -1.93877551 t = -2.056268035 + -1.93877551 Combine like terms: -2.056268035 + -1.93877551 = -3.995043545 t = -3.995043545 Simplifying t = -3.995043545Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.117492525, -3.995043545}
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