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Simplifying 4 = 13t + 0.5 * -9.8t2 Multiply 0.5 * -9.8 4 = 13t + -4.9t2 Solving 4 = 13t + -4.9t2 Solving for variable 't'. Reorder the terms: 4 + -13t + 4.9t2 = 13t + -13t + -4.9t2 + 4.9t2 Combine like terms: 13t + -13t = 0 4 + -13t + 4.9t2 = 0 + -4.9t2 + 4.9t2 4 + -13t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 4 + -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'. 0.8163265306 + -2.653061224t + t2 = 0 Move the constant term to the right: Add '-0.8163265306' to each side of the equation. 0.8163265306 + -2.653061224t + -0.8163265306 + t2 = 0 + -0.8163265306 Reorder the terms: 0.8163265306 + -0.8163265306 + -2.653061224t + t2 = 0 + -0.8163265306 Combine like terms: 0.8163265306 + -0.8163265306 = 0.0000000000 0.0000000000 + -2.653061224t + t2 = 0 + -0.8163265306 -2.653061224t + t2 = 0 + -0.8163265306 Combine like terms: 0 + -0.8163265306 = -0.8163265306 -2.653061224t + t2 = -0.8163265306 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 = -0.8163265306 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224t + t2 = -0.8163265306 + 1.759683465 Combine like terms: -0.8163265306 + 1.759683465 = 0.9433569344 1.759683465 + -2.653061224t + t2 = 0.9433569344 Factor a perfect square on the left side: (t + -1.326530612)(t + -1.326530612) = 0.9433569344 Calculate the square root of the right side: 0.971265635 Break this problem into two subproblems by setting (t + -1.326530612) equal to 0.971265635 and -0.971265635.Subproblem 1
t + -1.326530612 = 0.971265635 Simplifying t + -1.326530612 = 0.971265635 Reorder the terms: -1.326530612 + t = 0.971265635 Solving -1.326530612 + t = 0.971265635 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 = 0.971265635 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = 0.971265635 + 1.326530612 t = 0.971265635 + 1.326530612 Combine like terms: 0.971265635 + 1.326530612 = 2.297796247 t = 2.297796247 Simplifying t = 2.297796247Subproblem 2
t + -1.326530612 = -0.971265635 Simplifying t + -1.326530612 = -0.971265635 Reorder the terms: -1.326530612 + t = -0.971265635 Solving -1.326530612 + t = -0.971265635 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 = -0.971265635 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + t = -0.971265635 + 1.326530612 t = -0.971265635 + 1.326530612 Combine like terms: -0.971265635 + 1.326530612 = 0.355264977 t = 0.355264977 Simplifying t = 0.355264977Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.297796247, 0.355264977}
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