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Simplifying 14.4769t + -4.9t2 = 6 Solving 14.4769t + -4.9t2 = 6 Solving for variable 't'. Reorder the terms: -6 + 14.4769t + -4.9t2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 14.4769t + -4.9t2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 1.224489796 + -2.954469388t + t2 = 0 Move the constant term to the right: Add '-1.224489796' to each side of the equation. 1.224489796 + -2.954469388t + -1.224489796 + t2 = 0 + -1.224489796 Reorder the terms: 1.224489796 + -1.224489796 + -2.954469388t + t2 = 0 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + -2.954469388t + t2 = 0 + -1.224489796 -2.954469388t + t2 = 0 + -1.224489796 Combine like terms: 0 + -1.224489796 = -1.224489796 -2.954469388t + t2 = -1.224489796 The t term is -2.954469388t. Take half its coefficient (-1.477234694). Square it (2.182222341) and add it to both sides. Add '2.182222341' to each side of the equation. -2.954469388t + 2.182222341 + t2 = -1.224489796 + 2.182222341 Reorder the terms: 2.182222341 + -2.954469388t + t2 = -1.224489796 + 2.182222341 Combine like terms: -1.224489796 + 2.182222341 = 0.957732545 2.182222341 + -2.954469388t + t2 = 0.957732545 Factor a perfect square on the left side: (t + -1.477234694)(t + -1.477234694) = 0.957732545 Calculate the square root of the right side: 0.978638107 Break this problem into two subproblems by setting (t + -1.477234694) equal to 0.978638107 and -0.978638107.Subproblem 1
t + -1.477234694 = 0.978638107 Simplifying t + -1.477234694 = 0.978638107 Reorder the terms: -1.477234694 + t = 0.978638107 Solving -1.477234694 + t = 0.978638107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.477234694' to each side of the equation. -1.477234694 + 1.477234694 + t = 0.978638107 + 1.477234694 Combine like terms: -1.477234694 + 1.477234694 = 0.000000000 0.000000000 + t = 0.978638107 + 1.477234694 t = 0.978638107 + 1.477234694 Combine like terms: 0.978638107 + 1.477234694 = 2.455872801 t = 2.455872801 Simplifying t = 2.455872801Subproblem 2
t + -1.477234694 = -0.978638107 Simplifying t + -1.477234694 = -0.978638107 Reorder the terms: -1.477234694 + t = -0.978638107 Solving -1.477234694 + t = -0.978638107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.477234694' to each side of the equation. -1.477234694 + 1.477234694 + t = -0.978638107 + 1.477234694 Combine like terms: -1.477234694 + 1.477234694 = 0.000000000 0.000000000 + t = -0.978638107 + 1.477234694 t = -0.978638107 + 1.477234694 Combine like terms: -0.978638107 + 1.477234694 = 0.498596587 t = 0.498596587 Simplifying t = 0.498596587Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.455872801, 0.498596587}
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