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Simplifying -4.9t2 + 9.1t + 1.4 = 0 Reorder the terms: 1.4 + 9.1t + -4.9t2 = 0 Solving 1.4 + 9.1t + -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'. -0.2857142857 + -1.857142857t + t2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -1.857142857t + 0.2857142857 + t2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -1.857142857t + t2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -1.857142857t + t2 = 0 + 0.2857142857 -1.857142857t + t2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -1.857142857t + t2 = 0.2857142857 The t term is -1.857142857t. Take half its coefficient (-0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. -1.857142857t + 0.8622448978 + t2 = 0.2857142857 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857t + t2 = 0.2857142857 + 0.8622448978 Combine like terms: 0.2857142857 + 0.8622448978 = 1.1479591835 0.8622448978 + -1.857142857t + t2 = 1.1479591835 Factor a perfect square on the left side: (t + -0.9285714285)(t + -0.9285714285) = 1.1479591835 Calculate the square root of the right side: 1.071428571 Break this problem into two subproblems by setting (t + -0.9285714285) equal to 1.071428571 and -1.071428571.Subproblem 1
t + -0.9285714285 = 1.071428571 Simplifying t + -0.9285714285 = 1.071428571 Reorder the terms: -0.9285714285 + t = 1.071428571 Solving -0.9285714285 + t = 1.071428571 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + t = 1.071428571 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + t = 1.071428571 + 0.9285714285 t = 1.071428571 + 0.9285714285 Combine like terms: 1.071428571 + 0.9285714285 = 1.9999999995 t = 1.9999999995 Simplifying t = 1.9999999995Subproblem 2
t + -0.9285714285 = -1.071428571 Simplifying t + -0.9285714285 = -1.071428571 Reorder the terms: -0.9285714285 + t = -1.071428571 Solving -0.9285714285 + t = -1.071428571 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + t = -1.071428571 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + t = -1.071428571 + 0.9285714285 t = -1.071428571 + 0.9285714285 Combine like terms: -1.071428571 + 0.9285714285 = -0.1428571425 t = -0.1428571425 Simplifying t = -0.1428571425Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.9999999995, -0.1428571425}
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