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Simplifying 4.9t2 + 12t + 0.6 = 0 Reorder the terms: 0.6 + 12t + 4.9t2 = 0 Solving 0.6 + 12t + 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'. 0.1224489796 + 2.448979592t + t2 = 0 Move the constant term to the right: Add '-0.1224489796' to each side of the equation. 0.1224489796 + 2.448979592t + -0.1224489796 + t2 = 0 + -0.1224489796 Reorder the terms: 0.1224489796 + -0.1224489796 + 2.448979592t + t2 = 0 + -0.1224489796 Combine like terms: 0.1224489796 + -0.1224489796 = 0.0000000000 0.0000000000 + 2.448979592t + t2 = 0 + -0.1224489796 2.448979592t + t2 = 0 + -0.1224489796 Combine like terms: 0 + -0.1224489796 = -0.1224489796 2.448979592t + t2 = -0.1224489796 The t term is 2.448979592t. Take half its coefficient (1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. 2.448979592t + 1.499375261 + t2 = -0.1224489796 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592t + t2 = -0.1224489796 + 1.499375261 Combine like terms: -0.1224489796 + 1.499375261 = 1.3769262814 1.499375261 + 2.448979592t + t2 = 1.3769262814 Factor a perfect square on the left side: (t + 1.224489796)(t + 1.224489796) = 1.3769262814 Calculate the square root of the right side: 1.173425022 Break this problem into two subproblems by setting (t + 1.224489796) equal to 1.173425022 and -1.173425022.Subproblem 1
t + 1.224489796 = 1.173425022 Simplifying t + 1.224489796 = 1.173425022 Reorder the terms: 1.224489796 + t = 1.173425022 Solving 1.224489796 + t = 1.173425022 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.224489796' to each side of the equation. 1.224489796 + -1.224489796 + t = 1.173425022 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = 1.173425022 + -1.224489796 t = 1.173425022 + -1.224489796 Combine like terms: 1.173425022 + -1.224489796 = -0.051064774 t = -0.051064774 Simplifying t = -0.051064774Subproblem 2
t + 1.224489796 = -1.173425022 Simplifying t + 1.224489796 = -1.173425022 Reorder the terms: 1.224489796 + t = -1.173425022 Solving 1.224489796 + t = -1.173425022 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.224489796' to each side of the equation. 1.224489796 + -1.224489796 + t = -1.173425022 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = -1.173425022 + -1.224489796 t = -1.173425022 + -1.224489796 Combine like terms: -1.173425022 + -1.224489796 = -2.397914818 t = -2.397914818 Simplifying t = -2.397914818Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.051064774, -2.397914818}
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