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Simplifying 0 = -7t2 + 10t + 5 Reorder the terms: 0 = 5 + 10t + -7t2 Solving 0 = 5 + 10t + -7t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -10t + 7t2 = 5 + 10t + -7t2 + -5 + -10t + 7t2 Reorder the terms: -5 + -10t + 7t2 = 5 + -5 + 10t + -10t + -7t2 + 7t2 Combine like terms: 5 + -5 = 0 -5 + -10t + 7t2 = 0 + 10t + -10t + -7t2 + 7t2 -5 + -10t + 7t2 = 10t + -10t + -7t2 + 7t2 Combine like terms: 10t + -10t = 0 -5 + -10t + 7t2 = 0 + -7t2 + 7t2 -5 + -10t + 7t2 = -7t2 + 7t2 Combine like terms: -7t2 + 7t2 = 0 -5 + -10t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -1.428571429t + t2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -1.428571429t + 0.7142857143 + t2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -1.428571429t + t2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -1.428571429t + t2 = 0 + 0.7142857143 -1.428571429t + t2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -1.428571429t + t2 = 0.7142857143 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 = 0.7142857143 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429t + t2 = 0.7142857143 + 0.5102040819 Combine like terms: 0.7142857143 + 0.5102040819 = 1.2244897962 0.5102040819 + -1.428571429t + t2 = 1.2244897962 Factor a perfect square on the left side: (t + -0.7142857145)(t + -0.7142857145) = 1.2244897962 Calculate the square root of the right side: 1.10656667 Break this problem into two subproblems by setting (t + -0.7142857145) equal to 1.10656667 and -1.10656667.Subproblem 1
t + -0.7142857145 = 1.10656667 Simplifying t + -0.7142857145 = 1.10656667 Reorder the terms: -0.7142857145 + t = 1.10656667 Solving -0.7142857145 + t = 1.10656667 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 = 1.10656667 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = 1.10656667 + 0.7142857145 t = 1.10656667 + 0.7142857145 Combine like terms: 1.10656667 + 0.7142857145 = 1.8208523845 t = 1.8208523845 Simplifying t = 1.8208523845Subproblem 2
t + -0.7142857145 = -1.10656667 Simplifying t + -0.7142857145 = -1.10656667 Reorder the terms: -0.7142857145 + t = -1.10656667 Solving -0.7142857145 + t = -1.10656667 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 = -1.10656667 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = -1.10656667 + 0.7142857145 t = -1.10656667 + 0.7142857145 Combine like terms: -1.10656667 + 0.7142857145 = -0.3922809555 t = -0.3922809555 Simplifying t = -0.3922809555Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8208523845, -0.3922809555}
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