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Simplifying 41x2 + 140x + -21 = 0 Reorder the terms: -21 + 140x + 41x2 = 0 Solving -21 + 140x + 41x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. -0.512195122 + 3.414634146x + x2 = 0 Move the constant term to the right: Add '0.512195122' to each side of the equation. -0.512195122 + 3.414634146x + 0.512195122 + x2 = 0 + 0.512195122 Reorder the terms: -0.512195122 + 0.512195122 + 3.414634146x + x2 = 0 + 0.512195122 Combine like terms: -0.512195122 + 0.512195122 = 0.000000000 0.000000000 + 3.414634146x + x2 = 0 + 0.512195122 3.414634146x + x2 = 0 + 0.512195122 Combine like terms: 0 + 0.512195122 = 0.512195122 3.414634146x + x2 = 0.512195122 The x term is 3.414634146x. Take half its coefficient (1.707317073). Square it (2.914931588) and add it to both sides. Add '2.914931588' to each side of the equation. 3.414634146x + 2.914931588 + x2 = 0.512195122 + 2.914931588 Reorder the terms: 2.914931588 + 3.414634146x + x2 = 0.512195122 + 2.914931588 Combine like terms: 0.512195122 + 2.914931588 = 3.42712671 2.914931588 + 3.414634146x + x2 = 3.42712671 Factor a perfect square on the left side: (x + 1.707317073)(x + 1.707317073) = 3.42712671 Calculate the square root of the right side: 1.85125004 Break this problem into two subproblems by setting (x + 1.707317073) equal to 1.85125004 and -1.85125004.Subproblem 1
x + 1.707317073 = 1.85125004 Simplifying x + 1.707317073 = 1.85125004 Reorder the terms: 1.707317073 + x = 1.85125004 Solving 1.707317073 + x = 1.85125004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.707317073' to each side of the equation. 1.707317073 + -1.707317073 + x = 1.85125004 + -1.707317073 Combine like terms: 1.707317073 + -1.707317073 = 0.000000000 0.000000000 + x = 1.85125004 + -1.707317073 x = 1.85125004 + -1.707317073 Combine like terms: 1.85125004 + -1.707317073 = 0.143932967 x = 0.143932967 Simplifying x = 0.143932967Subproblem 2
x + 1.707317073 = -1.85125004 Simplifying x + 1.707317073 = -1.85125004 Reorder the terms: 1.707317073 + x = -1.85125004 Solving 1.707317073 + x = -1.85125004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.707317073' to each side of the equation. 1.707317073 + -1.707317073 + x = -1.85125004 + -1.707317073 Combine like terms: 1.707317073 + -1.707317073 = 0.000000000 0.000000000 + x = -1.85125004 + -1.707317073 x = -1.85125004 + -1.707317073 Combine like terms: -1.85125004 + -1.707317073 = -3.558567113 x = -3.558567113 Simplifying x = -3.558567113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.143932967, -3.558567113}
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