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Simplifying -4.9t2 + -7t + 950 = 0 Reorder the terms: 950 + -7t + -4.9t2 = 0 Solving 950 + -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'. -193.877551 + 1.428571429t + t2 = 0 Move the constant term to the right: Add '193.877551' to each side of the equation. -193.877551 + 1.428571429t + 193.877551 + t2 = 0 + 193.877551 Reorder the terms: -193.877551 + 193.877551 + 1.428571429t + t2 = 0 + 193.877551 Combine like terms: -193.877551 + 193.877551 = 0.000000 0.000000 + 1.428571429t + t2 = 0 + 193.877551 1.428571429t + t2 = 0 + 193.877551 Combine like terms: 0 + 193.877551 = 193.877551 1.428571429t + t2 = 193.877551 The t term is 1.428571429t. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429t + 0.5102040819 + t2 = 193.877551 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429t + t2 = 193.877551 + 0.5102040819 Combine like terms: 193.877551 + 0.5102040819 = 194.3877550819 0.5102040819 + 1.428571429t + t2 = 194.3877550819 Factor a perfect square on the left side: (t + 0.7142857145)(t + 0.7142857145) = 194.3877550819 Calculate the square root of the right side: 13.942300925 Break this problem into two subproblems by setting (t + 0.7142857145) equal to 13.942300925 and -13.942300925.Subproblem 1
t + 0.7142857145 = 13.942300925 Simplifying t + 0.7142857145 = 13.942300925 Reorder the terms: 0.7142857145 + t = 13.942300925 Solving 0.7142857145 + t = 13.942300925 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + t = 13.942300925 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = 13.942300925 + -0.7142857145 t = 13.942300925 + -0.7142857145 Combine like terms: 13.942300925 + -0.7142857145 = 13.2280152105 t = 13.2280152105 Simplifying t = 13.2280152105Subproblem 2
t + 0.7142857145 = -13.942300925 Simplifying t + 0.7142857145 = -13.942300925 Reorder the terms: 0.7142857145 + t = -13.942300925 Solving 0.7142857145 + t = -13.942300925 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + t = -13.942300925 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = -13.942300925 + -0.7142857145 t = -13.942300925 + -0.7142857145 Combine like terms: -13.942300925 + -0.7142857145 = -14.6565866395 t = -14.6565866395 Simplifying t = -14.6565866395Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.2280152105, -14.6565866395}
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