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Simplifying 0 = 1 + 28.7t + -1(0.5 * 9.8)(t2) Multiply 0.5 * 9.8 0 = 1 + 28.7t + -1(4.9)(t2) Multiply -1 * 4.9 0 = 1 + 28.7t + -4.9t2 Solving 0 = 1 + 28.7t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -28.7t + 4.9t2 = 1 + 28.7t + -4.9t2 + -1 + -28.7t + 4.9t2 Reorder the terms: -1 + -28.7t + 4.9t2 = 1 + -1 + 28.7t + -28.7t + -4.9t2 + 4.9t2 Combine like terms: 1 + -1 = 0 -1 + -28.7t + 4.9t2 = 0 + 28.7t + -28.7t + -4.9t2 + 4.9t2 -1 + -28.7t + 4.9t2 = 28.7t + -28.7t + -4.9t2 + 4.9t2 Combine like terms: 28.7t + -28.7t = 0.0 -1 + -28.7t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -1 + -28.7t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1 + -28.7t + 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'. -0.2040816327 + -5.857142857t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -5.857142857t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -5.857142857t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -5.857142857t + t2 = 0 + 0.2040816327 -5.857142857t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -5.857142857t + t2 = 0.2040816327 The t term is -5.857142857t. Take half its coefficient (-2.928571429). Square it (8.576530615) and add it to both sides. Add '8.576530615' to each side of the equation. -5.857142857t + 8.576530615 + t2 = 0.2040816327 + 8.576530615 Reorder the terms: 8.576530615 + -5.857142857t + t2 = 0.2040816327 + 8.576530615 Combine like terms: 0.2040816327 + 8.576530615 = 8.7806122477 8.576530615 + -5.857142857t + t2 = 8.7806122477 Factor a perfect square on the left side: (t + -2.928571429)(t + -2.928571429) = 8.7806122477 Calculate the square root of the right side: 2.963209788 Break this problem into two subproblems by setting (t + -2.928571429) equal to 2.963209788 and -2.963209788.Subproblem 1
t + -2.928571429 = 2.963209788 Simplifying t + -2.928571429 = 2.963209788 Reorder the terms: -2.928571429 + t = 2.963209788 Solving -2.928571429 + t = 2.963209788 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.928571429' to each side of the equation. -2.928571429 + 2.928571429 + t = 2.963209788 + 2.928571429 Combine like terms: -2.928571429 + 2.928571429 = 0.000000000 0.000000000 + t = 2.963209788 + 2.928571429 t = 2.963209788 + 2.928571429 Combine like terms: 2.963209788 + 2.928571429 = 5.891781217 t = 5.891781217 Simplifying t = 5.891781217Subproblem 2
t + -2.928571429 = -2.963209788 Simplifying t + -2.928571429 = -2.963209788 Reorder the terms: -2.928571429 + t = -2.963209788 Solving -2.928571429 + t = -2.963209788 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.928571429' to each side of the equation. -2.928571429 + 2.928571429 + t = -2.963209788 + 2.928571429 Combine like terms: -2.928571429 + 2.928571429 = 0.000000000 0.000000000 + t = -2.963209788 + 2.928571429 t = -2.963209788 + 2.928571429 Combine like terms: -2.963209788 + 2.928571429 = -0.034638359 t = -0.034638359 Simplifying t = -0.034638359Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.891781217, -0.034638359}
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