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Simplifying 7x2 + 29x + 6 = 0 Reorder the terms: 6 + 29x + 7x2 = 0 Solving 6 + 29x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 4.142857143x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 4.142857143x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 4.142857143x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 4.142857143x + x2 = 0 + -0.8571428571 4.142857143x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 4.142857143x + x2 = -0.8571428571 The x term is 4.142857143x. Take half its coefficient (2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. 4.142857143x + 4.290816329 + x2 = -0.8571428571 + 4.290816329 Reorder the terms: 4.290816329 + 4.142857143x + x2 = -0.8571428571 + 4.290816329 Combine like terms: -0.8571428571 + 4.290816329 = 3.4336734719 4.290816329 + 4.142857143x + x2 = 3.4336734719 Factor a perfect square on the left side: (x + 2.071428572)(x + 2.071428572) = 3.4336734719 Calculate the square root of the right side: 1.853017397 Break this problem into two subproblems by setting (x + 2.071428572) equal to 1.853017397 and -1.853017397.Subproblem 1
x + 2.071428572 = 1.853017397 Simplifying x + 2.071428572 = 1.853017397 Reorder the terms: 2.071428572 + x = 1.853017397 Solving 2.071428572 + x = 1.853017397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + x = 1.853017397 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = 1.853017397 + -2.071428572 x = 1.853017397 + -2.071428572 Combine like terms: 1.853017397 + -2.071428572 = -0.218411175 x = -0.218411175 Simplifying x = -0.218411175Subproblem 2
x + 2.071428572 = -1.853017397 Simplifying x + 2.071428572 = -1.853017397 Reorder the terms: 2.071428572 + x = -1.853017397 Solving 2.071428572 + x = -1.853017397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.071428572' to each side of the equation. 2.071428572 + -2.071428572 + x = -1.853017397 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = -1.853017397 + -2.071428572 x = -1.853017397 + -2.071428572 Combine like terms: -1.853017397 + -2.071428572 = -3.924445969 x = -3.924445969 Simplifying x = -3.924445969Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.218411175, -3.924445969}
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