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Simplifying 7t2 + 41t + 6 = 0 Reorder the terms: 6 + 41t + 7t2 = 0 Solving 6 + 41t + 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 + 5.857142857t + t2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 5.857142857t + -0.8571428571 + t2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 5.857142857t + t2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 5.857142857t + t2 = 0 + -0.8571428571 5.857142857t + t2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 5.857142857t + t2 = -0.8571428571 The t term is 5.857142857t. Take half its coefficient (2.928571429). Square it (8.576530615) and add it to both sides. Add '8.576530615' to each side of the equation. 5.857142857t + 8.576530615 + t2 = -0.8571428571 + 8.576530615 Reorder the terms: 8.576530615 + 5.857142857t + t2 = -0.8571428571 + 8.576530615 Combine like terms: -0.8571428571 + 8.576530615 = 7.7193877579 8.576530615 + 5.857142857t + t2 = 7.7193877579 Factor a perfect square on the left side: (t + 2.928571429)(t + 2.928571429) = 7.7193877579 Calculate the square root of the right side: 2.77837862 Break this problem into two subproblems by setting (t + 2.928571429) equal to 2.77837862 and -2.77837862.Subproblem 1
t + 2.928571429 = 2.77837862 Simplifying t + 2.928571429 = 2.77837862 Reorder the terms: 2.928571429 + t = 2.77837862 Solving 2.928571429 + t = 2.77837862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.928571429' to each side of the equation. 2.928571429 + -2.928571429 + t = 2.77837862 + -2.928571429 Combine like terms: 2.928571429 + -2.928571429 = 0.000000000 0.000000000 + t = 2.77837862 + -2.928571429 t = 2.77837862 + -2.928571429 Combine like terms: 2.77837862 + -2.928571429 = -0.150192809 t = -0.150192809 Simplifying t = -0.150192809Subproblem 2
t + 2.928571429 = -2.77837862 Simplifying t + 2.928571429 = -2.77837862 Reorder the terms: 2.928571429 + t = -2.77837862 Solving 2.928571429 + t = -2.77837862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.928571429' to each side of the equation. 2.928571429 + -2.928571429 + t = -2.77837862 + -2.928571429 Combine like terms: 2.928571429 + -2.928571429 = 0.000000000 0.000000000 + t = -2.77837862 + -2.928571429 t = -2.77837862 + -2.928571429 Combine like terms: -2.77837862 + -2.928571429 = -5.706950049 t = -5.706950049 Simplifying t = -5.706950049Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.150192809, -5.706950049}
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