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Simplifying 0 = -4.9t2 + 13t + 300 Reorder the terms: 0 = 300 + 13t + -4.9t2 Solving 0 = 300 + 13t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -300 = -300 -300 + -13t + 4.9t2 = 300 + 13t + -4.9t2 + -300 + -13t + 4.9t2 Reorder the terms: -300 + -13t + 4.9t2 = 300 + -300 + 13t + -13t + -4.9t2 + 4.9t2 Combine like terms: 300 + -300 = 0 -300 + -13t + 4.9t2 = 0 + 13t + -13t + -4.9t2 + 4.9t2 -300 + -13t + 4.9t2 = 13t + -13t + -4.9t2 + 4.9t2 Combine like terms: 13t + -13t = 0 -300 + -13t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -300 + -13t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -300 + -13t + 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'. -61.2244898 + -2.653061224t + t2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + -2.653061224t + 61.2244898 + t2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + -2.653061224t + t2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + -2.653061224t + t2 = 0 + 61.2244898 -2.653061224t + t2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 -2.653061224t + t2 = 61.2244898 The t term is -2.653061224t. Take half its coefficient (-1.326530612). Square it (1.759683465) and add it to both sides. Add '1.759683465' to each side of the equation. -2.653061224t + 1.759683465 + t2 = 61.2244898 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224t + t2 = 61.2244898 + 1.759683465 Combine like terms: 61.2244898 + 1.759683465 = 62.984173265 1.759683465 + -2.653061224t + t2 = 62.984173265 Factor a perfect square on the left side: (t + -1.326530612)(t + -1.326530612) = 62.984173265 Calculate the square root of the right side: 7.93625688 Break this problem into two subproblems by setting (t + -1.326530612) equal to 7.93625688 and -7.93625688.Subproblem 1
t + -1.326530612 = 7.93625688 Simplifying t + -1.326530612 = 7.93625688 Reorder the terms: -1.326530612 + t = 7.93625688 Solving -1.326530612 + t = 7.93625688 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + t = 7.93625688 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = 7.93625688 + 1.326530612 t = 7.93625688 + 1.326530612 Combine like terms: 7.93625688 + 1.326530612 = 9.262787492 t = 9.262787492 Simplifying t = 9.262787492Subproblem 2
t + -1.326530612 = -7.93625688 Simplifying t + -1.326530612 = -7.93625688 Reorder the terms: -1.326530612 + t = -7.93625688 Solving -1.326530612 + t = -7.93625688 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + t = -7.93625688 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = -7.93625688 + 1.326530612 t = -7.93625688 + 1.326530612 Combine like terms: -7.93625688 + 1.326530612 = -6.609726268 t = -6.609726268 Simplifying t = -6.609726268Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.262787492, -6.609726268}
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