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Simplifying 7t2 + 5t + -5 = 0 Reorder the terms: -5 + 5t + 7t2 = 0 Solving -5 + 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'. -0.7142857143 + 0.7142857143t + t2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.7142857143t + 0.7142857143 + t2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.7142857143t + t2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.7142857143t + t2 = 0 + 0.7142857143 0.7142857143t + t2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.7142857143t + t2 = 0.7142857143 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 = 0.7142857143 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143t + t2 = 0.7142857143 + 0.1275510204 Combine like terms: 0.7142857143 + 0.1275510204 = 0.8418367347 0.1275510204 + 0.7142857143t + t2 = 0.8418367347 Factor a perfect square on the left side: (t + 0.3571428572)(t + 0.3571428572) = 0.8418367347 Calculate the square root of the right side: 0.917516613 Break this problem into two subproblems by setting (t + 0.3571428572) equal to 0.917516613 and -0.917516613.Subproblem 1
t + 0.3571428572 = 0.917516613 Simplifying t + 0.3571428572 = 0.917516613 Reorder the terms: 0.3571428572 + t = 0.917516613 Solving 0.3571428572 + t = 0.917516613 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 = 0.917516613 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + t = 0.917516613 + -0.3571428572 t = 0.917516613 + -0.3571428572 Combine like terms: 0.917516613 + -0.3571428572 = 0.5603737558 t = 0.5603737558 Simplifying t = 0.5603737558Subproblem 2
t + 0.3571428572 = -0.917516613 Simplifying t + 0.3571428572 = -0.917516613 Reorder the terms: 0.3571428572 + t = -0.917516613 Solving 0.3571428572 + t = -0.917516613 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 = -0.917516613 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + t = -0.917516613 + -0.3571428572 t = -0.917516613 + -0.3571428572 Combine like terms: -0.917516613 + -0.3571428572 = -1.2746594702 t = -1.2746594702 Simplifying t = -1.2746594702Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.5603737558, -1.2746594702}
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