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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 = 5.1479591861 4.290816329 + 4.142857143x + x2 = 5.1479591861 Factor a perfect square on the left side: (x + 2.071428572)(x + 2.071428572) = 5.1479591861 Calculate the square root of the right side: 2.268911454 Break this problem into two subproblems by setting (x + 2.071428572) equal to 2.268911454 and -2.268911454.Subproblem 1
x + 2.071428572 = 2.268911454 Simplifying x + 2.071428572 = 2.268911454 Reorder the terms: 2.071428572 + x = 2.268911454 Solving 2.071428572 + x = 2.268911454 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 = 2.268911454 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = 2.268911454 + -2.071428572 x = 2.268911454 + -2.071428572 Combine like terms: 2.268911454 + -2.071428572 = 0.197482882 x = 0.197482882 Simplifying x = 0.197482882Subproblem 2
x + 2.071428572 = -2.268911454 Simplifying x + 2.071428572 = -2.268911454 Reorder the terms: 2.071428572 + x = -2.268911454 Solving 2.071428572 + x = -2.268911454 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 = -2.268911454 + -2.071428572 Combine like terms: 2.071428572 + -2.071428572 = 0.000000000 0.000000000 + x = -2.268911454 + -2.071428572 x = -2.268911454 + -2.071428572 Combine like terms: -2.268911454 + -2.071428572 = -4.340340026 x = -4.340340026 Simplifying x = -4.340340026Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.197482882, -4.340340026}
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