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Simplifying -2.3 = 6.18t + -4.9t2 Solving -2.3 = 6.18t + -4.9t2 Solving for variable 't'. Reorder the terms: -2.3 + -6.18t + 4.9t2 = 6.18t + -6.18t + -4.9t2 + 4.9t2 Combine like terms: 6.18t + -6.18t = 0.00 -2.3 + -6.18t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -2.3 + -6.18t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -2.3 + -6.18t + 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'. -0.4693877551 + -1.26122449t + t2 = 0 Move the constant term to the right: Add '0.4693877551' to each side of the equation. -0.4693877551 + -1.26122449t + 0.4693877551 + t2 = 0 + 0.4693877551 Reorder the terms: -0.4693877551 + 0.4693877551 + -1.26122449t + t2 = 0 + 0.4693877551 Combine like terms: -0.4693877551 + 0.4693877551 = 0.0000000000 0.0000000000 + -1.26122449t + t2 = 0 + 0.4693877551 -1.26122449t + t2 = 0 + 0.4693877551 Combine like terms: 0 + 0.4693877551 = 0.4693877551 -1.26122449t + t2 = 0.4693877551 The t term is -1.26122449t. Take half its coefficient (-0.630612245). Square it (0.3976718035) and add it to both sides. Add '0.3976718035' to each side of the equation. -1.26122449t + 0.3976718035 + t2 = 0.4693877551 + 0.3976718035 Reorder the terms: 0.3976718035 + -1.26122449t + t2 = 0.4693877551 + 0.3976718035 Combine like terms: 0.4693877551 + 0.3976718035 = 0.8670595586 0.3976718035 + -1.26122449t + t2 = 0.8670595586 Factor a perfect square on the left side: (t + -0.630612245)(t + -0.630612245) = 0.8670595586 Calculate the square root of the right side: 0.931160329 Break this problem into two subproblems by setting (t + -0.630612245) equal to 0.931160329 and -0.931160329.Subproblem 1
t + -0.630612245 = 0.931160329 Simplifying t + -0.630612245 = 0.931160329 Reorder the terms: -0.630612245 + t = 0.931160329 Solving -0.630612245 + t = 0.931160329 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.630612245' to each side of the equation. -0.630612245 + 0.630612245 + t = 0.931160329 + 0.630612245 Combine like terms: -0.630612245 + 0.630612245 = 0.000000000 0.000000000 + t = 0.931160329 + 0.630612245 t = 0.931160329 + 0.630612245 Combine like terms: 0.931160329 + 0.630612245 = 1.561772574 t = 1.561772574 Simplifying t = 1.561772574Subproblem 2
t + -0.630612245 = -0.931160329 Simplifying t + -0.630612245 = -0.931160329 Reorder the terms: -0.630612245 + t = -0.931160329 Solving -0.630612245 + t = -0.931160329 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.630612245' to each side of the equation. -0.630612245 + 0.630612245 + t = -0.931160329 + 0.630612245 Combine like terms: -0.630612245 + 0.630612245 = 0.000000000 0.000000000 + t = -0.931160329 + 0.630612245 t = -0.931160329 + 0.630612245 Combine like terms: -0.931160329 + 0.630612245 = -0.300548084 t = -0.300548084 Simplifying t = -0.300548084Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.561772574, -0.300548084}
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