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Simplifying 4.9t2 + 4916.7t + -350 = 0 Reorder the terms: -350 + 4916.7t + 4.9t2 = 0 Solving -350 + 4916.7t + 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'. -71.42857143 + 1003.408163t + t2 = 0 Move the constant term to the right: Add '71.42857143' to each side of the equation. -71.42857143 + 1003.408163t + 71.42857143 + t2 = 0 + 71.42857143 Reorder the terms: -71.42857143 + 71.42857143 + 1003.408163t + t2 = 0 + 71.42857143 Combine like terms: -71.42857143 + 71.42857143 = 0.00000000 0.00000000 + 1003.408163t + t2 = 0 + 71.42857143 1003.408163t + t2 = 0 + 71.42857143 Combine like terms: 0 + 71.42857143 = 71.42857143 1003.408163t + t2 = 71.42857143 The t term is 1003.408163t. Take half its coefficient (501.7040815). Square it (251706.9854) and add it to both sides. Add '251706.9854' to each side of the equation. 1003.408163t + 251706.9854 + t2 = 71.42857143 + 251706.9854 Reorder the terms: 251706.9854 + 1003.408163t + t2 = 71.42857143 + 251706.9854 Combine like terms: 71.42857143 + 251706.9854 = 251778.41397143 251706.9854 + 1003.408163t + t2 = 251778.41397143 Factor a perfect square on the left side: (t + 501.7040815)(t + 501.7040815) = 251778.41397143 Calculate the square root of the right side: 501.775262415 Break this problem into two subproblems by setting (t + 501.7040815) equal to 501.775262415 and -501.775262415.Subproblem 1
t + 501.7040815 = 501.775262415 Simplifying t + 501.7040815 = 501.775262415 Reorder the terms: 501.7040815 + t = 501.775262415 Solving 501.7040815 + t = 501.775262415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-501.7040815' to each side of the equation. 501.7040815 + -501.7040815 + t = 501.775262415 + -501.7040815 Combine like terms: 501.7040815 + -501.7040815 = 0.0000000 0.0000000 + t = 501.775262415 + -501.7040815 t = 501.775262415 + -501.7040815 Combine like terms: 501.775262415 + -501.7040815 = 0.071180915 t = 0.071180915 Simplifying t = 0.071180915Subproblem 2
t + 501.7040815 = -501.775262415 Simplifying t + 501.7040815 = -501.775262415 Reorder the terms: 501.7040815 + t = -501.775262415 Solving 501.7040815 + t = -501.775262415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-501.7040815' to each side of the equation. 501.7040815 + -501.7040815 + t = -501.775262415 + -501.7040815 Combine like terms: 501.7040815 + -501.7040815 = 0.0000000 0.0000000 + t = -501.775262415 + -501.7040815 t = -501.775262415 + -501.7040815 Combine like terms: -501.775262415 + -501.7040815 = -1003.479343915 t = -1003.479343915 Simplifying t = -1003.479343915Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.071180915, -1003.479343915}
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