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Simplifying 7.05t + 9.8t2 + -30.6 = 0 Reorder the terms: -30.6 + 7.05t + 9.8t2 = 0 Solving -30.6 + 7.05t + 9.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -3.12244898 + 0.7193877551t + t2 = 0 Move the constant term to the right: Add '3.12244898' to each side of the equation. -3.12244898 + 0.7193877551t + 3.12244898 + t2 = 0 + 3.12244898 Reorder the terms: -3.12244898 + 3.12244898 + 0.7193877551t + t2 = 0 + 3.12244898 Combine like terms: -3.12244898 + 3.12244898 = 0.00000000 0.00000000 + 0.7193877551t + t2 = 0 + 3.12244898 0.7193877551t + t2 = 0 + 3.12244898 Combine like terms: 0 + 3.12244898 = 3.12244898 0.7193877551t + t2 = 3.12244898 The t term is 0.7193877551t. Take half its coefficient (0.3596938776). Square it (0.1293796856) and add it to both sides. Add '0.1293796856' to each side of the equation. 0.7193877551t + 0.1293796856 + t2 = 3.12244898 + 0.1293796856 Reorder the terms: 0.1293796856 + 0.7193877551t + t2 = 3.12244898 + 0.1293796856 Combine like terms: 3.12244898 + 0.1293796856 = 3.2518286656 0.1293796856 + 0.7193877551t + t2 = 3.2518286656 Factor a perfect square on the left side: (t + 0.3596938776)(t + 0.3596938776) = 3.2518286656 Calculate the square root of the right side: 1.803282747 Break this problem into two subproblems by setting (t + 0.3596938776) equal to 1.803282747 and -1.803282747.Subproblem 1
t + 0.3596938776 = 1.803282747 Simplifying t + 0.3596938776 = 1.803282747 Reorder the terms: 0.3596938776 + t = 1.803282747 Solving 0.3596938776 + t = 1.803282747 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3596938776' to each side of the equation. 0.3596938776 + -0.3596938776 + t = 1.803282747 + -0.3596938776 Combine like terms: 0.3596938776 + -0.3596938776 = 0.0000000000 0.0000000000 + t = 1.803282747 + -0.3596938776 t = 1.803282747 + -0.3596938776 Combine like terms: 1.803282747 + -0.3596938776 = 1.4435888694 t = 1.4435888694 Simplifying t = 1.4435888694Subproblem 2
t + 0.3596938776 = -1.803282747 Simplifying t + 0.3596938776 = -1.803282747 Reorder the terms: 0.3596938776 + t = -1.803282747 Solving 0.3596938776 + t = -1.803282747 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3596938776' to each side of the equation. 0.3596938776 + -0.3596938776 + t = -1.803282747 + -0.3596938776 Combine like terms: 0.3596938776 + -0.3596938776 = 0.0000000000 0.0000000000 + t = -1.803282747 + -0.3596938776 t = -1.803282747 + -0.3596938776 Combine like terms: -1.803282747 + -0.3596938776 = -2.1629766246 t = -2.1629766246 Simplifying t = -2.1629766246Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.4435888694, -2.1629766246}
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