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Simplifying 24x2 + 29x + -8 = 0 Reorder the terms: -8 + 29x + 24x2 = 0 Solving -8 + 29x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.3333333333 + 1.208333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.208333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.208333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.208333333x + x2 = 0 + 0.3333333333 1.208333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.208333333x + x2 = 0.3333333333 The x term is 1.208333333x. Take half its coefficient (0.6041666665). Square it (0.3650173609) and add it to both sides. Add '0.3650173609' to each side of the equation. 1.208333333x + 0.3650173609 + x2 = 0.3333333333 + 0.3650173609 Reorder the terms: 0.3650173609 + 1.208333333x + x2 = 0.3333333333 + 0.3650173609 Combine like terms: 0.3333333333 + 0.3650173609 = 0.6983506942 0.3650173609 + 1.208333333x + x2 = 0.6983506942 Factor a perfect square on the left side: (x + 0.6041666665)(x + 0.6041666665) = 0.6983506942 Calculate the square root of the right side: 0.835673797 Break this problem into two subproblems by setting (x + 0.6041666665) equal to 0.835673797 and -0.835673797.Subproblem 1
x + 0.6041666665 = 0.835673797 Simplifying x + 0.6041666665 = 0.835673797 Reorder the terms: 0.6041666665 + x = 0.835673797 Solving 0.6041666665 + x = 0.835673797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6041666665' to each side of the equation. 0.6041666665 + -0.6041666665 + x = 0.835673797 + -0.6041666665 Combine like terms: 0.6041666665 + -0.6041666665 = 0.0000000000 0.0000000000 + x = 0.835673797 + -0.6041666665 x = 0.835673797 + -0.6041666665 Combine like terms: 0.835673797 + -0.6041666665 = 0.2315071305 x = 0.2315071305 Simplifying x = 0.2315071305Subproblem 2
x + 0.6041666665 = -0.835673797 Simplifying x + 0.6041666665 = -0.835673797 Reorder the terms: 0.6041666665 + x = -0.835673797 Solving 0.6041666665 + x = -0.835673797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6041666665' to each side of the equation. 0.6041666665 + -0.6041666665 + x = -0.835673797 + -0.6041666665 Combine like terms: 0.6041666665 + -0.6041666665 = 0.0000000000 0.0000000000 + x = -0.835673797 + -0.6041666665 x = -0.835673797 + -0.6041666665 Combine like terms: -0.835673797 + -0.6041666665 = -1.4398404635 x = -1.4398404635 Simplifying x = -1.4398404635Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2315071305, -1.4398404635}
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