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Simplifying 9.8t2 + 8.95t + -29 = 0 Reorder the terms: -29 + 8.95t + 9.8t2 = 0 Solving -29 + 8.95t + 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'. -2.959183673 + 0.9132653061t + t2 = 0 Move the constant term to the right: Add '2.959183673' to each side of the equation. -2.959183673 + 0.9132653061t + 2.959183673 + t2 = 0 + 2.959183673 Reorder the terms: -2.959183673 + 2.959183673 + 0.9132653061t + t2 = 0 + 2.959183673 Combine like terms: -2.959183673 + 2.959183673 = 0.000000000 0.000000000 + 0.9132653061t + t2 = 0 + 2.959183673 0.9132653061t + t2 = 0 + 2.959183673 Combine like terms: 0 + 2.959183673 = 2.959183673 0.9132653061t + t2 = 2.959183673 The t term is 0.9132653061t. Take half its coefficient (0.4566326531). Square it (0.2085133799) and add it to both sides. Add '0.2085133799' to each side of the equation. 0.9132653061t + 0.2085133799 + t2 = 2.959183673 + 0.2085133799 Reorder the terms: 0.2085133799 + 0.9132653061t + t2 = 2.959183673 + 0.2085133799 Combine like terms: 2.959183673 + 0.2085133799 = 3.1676970529 0.2085133799 + 0.9132653061t + t2 = 3.1676970529 Factor a perfect square on the left side: (t + 0.4566326531)(t + 0.4566326531) = 3.1676970529 Calculate the square root of the right side: 1.779802532 Break this problem into two subproblems by setting (t + 0.4566326531) equal to 1.779802532 and -1.779802532.Subproblem 1
t + 0.4566326531 = 1.779802532 Simplifying t + 0.4566326531 = 1.779802532 Reorder the terms: 0.4566326531 + t = 1.779802532 Solving 0.4566326531 + t = 1.779802532 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4566326531' to each side of the equation. 0.4566326531 + -0.4566326531 + t = 1.779802532 + -0.4566326531 Combine like terms: 0.4566326531 + -0.4566326531 = 0.0000000000 0.0000000000 + t = 1.779802532 + -0.4566326531 t = 1.779802532 + -0.4566326531 Combine like terms: 1.779802532 + -0.4566326531 = 1.3231698789 t = 1.3231698789 Simplifying t = 1.3231698789Subproblem 2
t + 0.4566326531 = -1.779802532 Simplifying t + 0.4566326531 = -1.779802532 Reorder the terms: 0.4566326531 + t = -1.779802532 Solving 0.4566326531 + t = -1.779802532 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4566326531' to each side of the equation. 0.4566326531 + -0.4566326531 + t = -1.779802532 + -0.4566326531 Combine like terms: 0.4566326531 + -0.4566326531 = 0.0000000000 0.0000000000 + t = -1.779802532 + -0.4566326531 t = -1.779802532 + -0.4566326531 Combine like terms: -1.779802532 + -0.4566326531 = -2.2364351851 t = -2.2364351851 Simplifying t = -2.2364351851Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3231698789, -2.2364351851}
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