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Simplifying 9.8t2 + -14t + -82 = 0 Reorder the terms: -82 + -14t + 9.8t2 = 0 Solving -82 + -14t + 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'. -8.367346939 + -1.428571429t + t2 = 0 Move the constant term to the right: Add '8.367346939' to each side of the equation. -8.367346939 + -1.428571429t + 8.367346939 + t2 = 0 + 8.367346939 Reorder the terms: -8.367346939 + 8.367346939 + -1.428571429t + t2 = 0 + 8.367346939 Combine like terms: -8.367346939 + 8.367346939 = 0.000000000 0.000000000 + -1.428571429t + t2 = 0 + 8.367346939 -1.428571429t + t2 = 0 + 8.367346939 Combine like terms: 0 + 8.367346939 = 8.367346939 -1.428571429t + t2 = 8.367346939 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 = 8.367346939 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429t + t2 = 8.367346939 + 0.5102040819 Combine like terms: 8.367346939 + 0.5102040819 = 8.8775510209 0.5102040819 + -1.428571429t + t2 = 8.8775510209 Factor a perfect square on the left side: (t + -0.7142857145)(t + -0.7142857145) = 8.8775510209 Calculate the square root of the right side: 2.979521945 Break this problem into two subproblems by setting (t + -0.7142857145) equal to 2.979521945 and -2.979521945.Subproblem 1
t + -0.7142857145 = 2.979521945 Simplifying t + -0.7142857145 = 2.979521945 Reorder the terms: -0.7142857145 + t = 2.979521945 Solving -0.7142857145 + t = 2.979521945 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 = 2.979521945 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = 2.979521945 + 0.7142857145 t = 2.979521945 + 0.7142857145 Combine like terms: 2.979521945 + 0.7142857145 = 3.6938076595 t = 3.6938076595 Simplifying t = 3.6938076595Subproblem 2
t + -0.7142857145 = -2.979521945 Simplifying t + -0.7142857145 = -2.979521945 Reorder the terms: -0.7142857145 + t = -2.979521945 Solving -0.7142857145 + t = -2.979521945 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 = -2.979521945 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = -2.979521945 + 0.7142857145 t = -2.979521945 + 0.7142857145 Combine like terms: -2.979521945 + 0.7142857145 = -2.2652362305 t = -2.2652362305 Simplifying t = -2.2652362305Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.6938076595, -2.2652362305}
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