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Simplifying 4.9t2 + -12.86t + 3.5 = 0 Reorder the terms: 3.5 + -12.86t + 4.9t2 = 0 Solving 3.5 + -12.86t + 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'. 0.7142857143 + -2.624489796t + t2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -2.624489796t + -0.7142857143 + t2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -2.624489796t + t2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -2.624489796t + t2 = 0 + -0.7142857143 -2.624489796t + t2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -2.624489796t + t2 = -0.7142857143 The t term is -2.624489796t. Take half its coefficient (-1.312244898). Square it (1.721986672) and add it to both sides. Add '1.721986672' to each side of the equation. -2.624489796t + 1.721986672 + t2 = -0.7142857143 + 1.721986672 Reorder the terms: 1.721986672 + -2.624489796t + t2 = -0.7142857143 + 1.721986672 Combine like terms: -0.7142857143 + 1.721986672 = 1.0077009577 1.721986672 + -2.624489796t + t2 = 1.0077009577 Factor a perfect square on the left side: (t + -1.312244898)(t + -1.312244898) = 1.0077009577 Calculate the square root of the right side: 1.003843094 Break this problem into two subproblems by setting (t + -1.312244898) equal to 1.003843094 and -1.003843094.Subproblem 1
t + -1.312244898 = 1.003843094 Simplifying t + -1.312244898 = 1.003843094 Reorder the terms: -1.312244898 + t = 1.003843094 Solving -1.312244898 + t = 1.003843094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.312244898' to each side of the equation. -1.312244898 + 1.312244898 + t = 1.003843094 + 1.312244898 Combine like terms: -1.312244898 + 1.312244898 = 0.000000000 0.000000000 + t = 1.003843094 + 1.312244898 t = 1.003843094 + 1.312244898 Combine like terms: 1.003843094 + 1.312244898 = 2.316087992 t = 2.316087992 Simplifying t = 2.316087992Subproblem 2
t + -1.312244898 = -1.003843094 Simplifying t + -1.312244898 = -1.003843094 Reorder the terms: -1.312244898 + t = -1.003843094 Solving -1.312244898 + t = -1.003843094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.312244898' to each side of the equation. -1.312244898 + 1.312244898 + t = -1.003843094 + 1.312244898 Combine like terms: -1.312244898 + 1.312244898 = 0.000000000 0.000000000 + t = -1.003843094 + 1.312244898 t = -1.003843094 + 1.312244898 Combine like terms: -1.003843094 + 1.312244898 = 0.308401804 t = 0.308401804 Simplifying t = 0.308401804Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.316087992, 0.308401804}
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