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Simplifying 7t2 + -5t + -6 = 0 Reorder the terms: -6 + -5t + 7t2 = 0 Solving -6 + -5t + 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 + -0.7142857143t + t2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -0.7142857143t + 0.8571428571 + t2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -0.7142857143t + t2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -0.7142857143t + t2 = 0 + 0.8571428571 -0.7142857143t + t2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -0.7142857143t + t2 = 0.8571428571 The t term is -0.7142857143t. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143t + 0.1275510204 + t2 = 0.8571428571 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143t + t2 = 0.8571428571 + 0.1275510204 Combine like terms: 0.8571428571 + 0.1275510204 = 0.9846938775 0.1275510204 + -0.7142857143t + t2 = 0.9846938775 Factor a perfect square on the left side: (t + -0.3571428572)(t + -0.3571428572) = 0.9846938775 Calculate the square root of the right side: 0.992317428 Break this problem into two subproblems by setting (t + -0.3571428572) equal to 0.992317428 and -0.992317428.Subproblem 1
t + -0.3571428572 = 0.992317428 Simplifying t + -0.3571428572 = 0.992317428 Reorder the terms: -0.3571428572 + t = 0.992317428 Solving -0.3571428572 + t = 0.992317428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + t = 0.992317428 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + t = 0.992317428 + 0.3571428572 t = 0.992317428 + 0.3571428572 Combine like terms: 0.992317428 + 0.3571428572 = 1.3494602852 t = 1.3494602852 Simplifying t = 1.3494602852Subproblem 2
t + -0.3571428572 = -0.992317428 Simplifying t + -0.3571428572 = -0.992317428 Reorder the terms: -0.3571428572 + t = -0.992317428 Solving -0.3571428572 + t = -0.992317428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + t = -0.992317428 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + t = -0.992317428 + 0.3571428572 t = -0.992317428 + 0.3571428572 Combine like terms: -0.992317428 + 0.3571428572 = -0.6351745708 t = -0.6351745708 Simplifying t = -0.6351745708Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3494602852, -0.6351745708}
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