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Simplifying 4.9t2 + -15.2169t = 0.395 Reorder the terms: -15.2169t + 4.9t2 = 0.395 Solving -15.2169t + 4.9t2 = 0.395 Solving for variable 't'. Reorder the terms: -0.395 + -15.2169t + 4.9t2 = 0.395 + -0.395 Combine like terms: 0.395 + -0.395 = 0.000 -0.395 + -15.2169t + 4.9t2 = 0.000 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 = 0.00 Move the constant term to the right: Add '0.0806122449' to each side of the equation. -0.0806122449 + -3.105489796t + 0.0806122449 + t2 = 0.00 + 0.0806122449 Reorder the terms: -0.0806122449 + 0.0806122449 + -3.105489796t + t2 = 0.00 + 0.0806122449 Combine like terms: -0.0806122449 + 0.0806122449 = 0.0000000000 0.0000000000 + -3.105489796t + t2 = 0.00 + 0.0806122449 -3.105489796t + t2 = 0.00 + 0.0806122449 Combine like terms: 0.00 + 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 = 2.4916289629 2.411016718 + -3.105489796t + t2 = 2.4916289629 Factor a perfect square on the left side: (t + -1.552744898)(t + -1.552744898) = 2.4916289629 Calculate the square root of the right side: 1.578489456 Break this problem into two subproblems by setting (t + -1.552744898) equal to 1.578489456 and -1.578489456.Subproblem 1
t + -1.552744898 = 1.578489456 Simplifying t + -1.552744898 = 1.578489456 Reorder the terms: -1.552744898 + t = 1.578489456 Solving -1.552744898 + t = 1.578489456 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 = 1.578489456 + 1.552744898 Combine like terms: -1.552744898 + 1.552744898 = 0.000000000 0.000000000 + t = 1.578489456 + 1.552744898 t = 1.578489456 + 1.552744898 Combine like terms: 1.578489456 + 1.552744898 = 3.131234354 t = 3.131234354 Simplifying t = 3.131234354Subproblem 2
t + -1.552744898 = -1.578489456 Simplifying t + -1.552744898 = -1.578489456 Reorder the terms: -1.552744898 + t = -1.578489456 Solving -1.552744898 + t = -1.578489456 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 = -1.578489456 + 1.552744898 Combine like terms: -1.552744898 + 1.552744898 = 0.000000000 0.000000000 + t = -1.578489456 + 1.552744898 t = -1.578489456 + 1.552744898 Combine like terms: -1.578489456 + 1.552744898 = -0.025744558 t = -0.025744558 Simplifying t = -0.025744558Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.131234354, -0.025744558}
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