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Simplifying 4.9t2 + -15.2169t + 0.395 = 0 Reorder the terms: 0.395 + -15.2169t + 4.9t2 = 0 Solving 0.395 + -15.2169t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.0806122449 + -3.105489796t + t2 = 0 Move the constant term to the right: Add '-0.0806122449' to each side of the equation. 0.0806122449 + -3.105489796t + -0.0806122449 + t2 = 0 + -0.0806122449 Reorder the terms: 0.0806122449 + -0.0806122449 + -3.105489796t + t2 = 0 + -0.0806122449 Combine like terms: 0.0806122449 + -0.0806122449 = 0.0000000000 0.0000000000 + -3.105489796t + t2 = 0 + -0.0806122449 -3.105489796t + t2 = 0 + -0.0806122449 Combine like terms: 0 + -0.0806122449 = -0.0806122449 -3.105489796t + t2 = -0.0806122449 The t term is -3.105489796t. Take half its coefficient (-1.552744898). Square it (2.411016718) and add it to both sides. Add '2.411016718' to each side of the equation. -3.105489796t + 2.411016718 + t2 = -0.0806122449 + 2.411016718 Reorder the terms: 2.411016718 + -3.105489796t + t2 = -0.0806122449 + 2.411016718 Combine like terms: -0.0806122449 + 2.411016718 = 2.3304044731 2.411016718 + -3.105489796t + t2 = 2.3304044731 Factor a perfect square on the left side: (t + -1.552744898)(t + -1.552744898) = 2.3304044731 Calculate the square root of the right side: 1.526566236 Break this problem into two subproblems by setting (t + -1.552744898) equal to 1.526566236 and -1.526566236.Subproblem 1
t + -1.552744898 = 1.526566236 Simplifying t + -1.552744898 = 1.526566236 Reorder the terms: -1.552744898 + t = 1.526566236 Solving -1.552744898 + t = 1.526566236 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.552744898' to each side of the equation. -1.552744898 + 1.552744898 + t = 1.526566236 + 1.552744898 Combine like terms: -1.552744898 + 1.552744898 = 0.000000000 0.000000000 + t = 1.526566236 + 1.552744898 t = 1.526566236 + 1.552744898 Combine like terms: 1.526566236 + 1.552744898 = 3.079311134 t = 3.079311134 Simplifying t = 3.079311134Subproblem 2
t + -1.552744898 = -1.526566236 Simplifying t + -1.552744898 = -1.526566236 Reorder the terms: -1.552744898 + t = -1.526566236 Solving -1.552744898 + t = -1.526566236 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.552744898' to each side of the equation. -1.552744898 + 1.552744898 + t = -1.526566236 + 1.552744898 Combine like terms: -1.552744898 + 1.552744898 = 0.000000000 0.000000000 + t = -1.526566236 + 1.552744898 t = -1.526566236 + 1.552744898 Combine like terms: -1.526566236 + 1.552744898 = 0.026178662 t = 0.026178662 Simplifying t = 0.026178662Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.079311134, 0.026178662}
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