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Simplifying 7t2 + -15t + 6 = 0 Reorder the terms: 6 + -15t + 7t2 = 0 Solving 6 + -15t + 7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + -2.142857143t + t2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -2.142857143t + -0.8571428571 + t2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -2.142857143t + t2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -2.142857143t + t2 = 0 + -0.8571428571 -2.142857143t + t2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -2.142857143t + t2 = -0.8571428571 The t term is -2.142857143t. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143t + 1.147959185 + t2 = -0.8571428571 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143t + t2 = -0.8571428571 + 1.147959185 Combine like terms: -0.8571428571 + 1.147959185 = 0.2908163279 1.147959185 + -2.142857143t + t2 = 0.2908163279 Factor a perfect square on the left side: (t + -1.071428572)(t + -1.071428572) = 0.2908163279 Calculate the square root of the right side: 0.53927389 Break this problem into two subproblems by setting (t + -1.071428572) equal to 0.53927389 and -0.53927389.Subproblem 1
t + -1.071428572 = 0.53927389 Simplifying t + -1.071428572 = 0.53927389 Reorder the terms: -1.071428572 + t = 0.53927389 Solving -1.071428572 + t = 0.53927389 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + t = 0.53927389 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + t = 0.53927389 + 1.071428572 t = 0.53927389 + 1.071428572 Combine like terms: 0.53927389 + 1.071428572 = 1.610702462 t = 1.610702462 Simplifying t = 1.610702462Subproblem 2
t + -1.071428572 = -0.53927389 Simplifying t + -1.071428572 = -0.53927389 Reorder the terms: -1.071428572 + t = -0.53927389 Solving -1.071428572 + t = -0.53927389 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + t = -0.53927389 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + t = -0.53927389 + 1.071428572 t = -0.53927389 + 1.071428572 Combine like terms: -0.53927389 + 1.071428572 = 0.532154682 t = 0.532154682 Simplifying t = 0.532154682Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.610702462, 0.532154682}
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