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Simplifying 4.9t2 + t + -14 = 0 Reorder the terms: -14 + t + 4.9t2 = 0 Solving -14 + t + 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'. -2.857142857 + 0.2040816327t + t2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 0.2040816327t + 2.857142857 + t2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 0.2040816327t + t2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 0.2040816327t + t2 = 0 + 2.857142857 0.2040816327t + t2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 0.2040816327t + t2 = 2.857142857 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2040816327t + 0.25 + t2 = 2.857142857 + 0.25 Reorder the terms: 0.25 + 0.2040816327t + t2 = 2.857142857 + 0.25 Combine like terms: 2.857142857 + 0.25 = 3.107142857 0.25 + 0.2040816327t + t2 = 3.107142857 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 3.107142857 Calculate the square root of the right side: 1.762708954 Break this problem into two subproblems by setting (t + 0.5) equal to 1.762708954 and -1.762708954.Subproblem 1
t + 0.5 = 1.762708954 Simplifying t + 0.5 = 1.762708954 Reorder the terms: 0.5 + t = 1.762708954 Solving 0.5 + t = 1.762708954 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 1.762708954 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.762708954 + -0.5 t = 1.762708954 + -0.5 Combine like terms: 1.762708954 + -0.5 = 1.262708954 t = 1.262708954 Simplifying t = 1.262708954Subproblem 2
t + 0.5 = -1.762708954 Simplifying t + 0.5 = -1.762708954 Reorder the terms: 0.5 + t = -1.762708954 Solving 0.5 + t = -1.762708954 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -1.762708954 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.762708954 + -0.5 t = -1.762708954 + -0.5 Combine like terms: -1.762708954 + -0.5 = -2.262708954 t = -2.262708954 Simplifying t = -2.262708954Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.262708954, -2.262708954}
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