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Simplifying 8086248x2 + -8142129x + 55880 = 0 Reorder the terms: 55880 + -8142129x + 8086248x2 = 0 Solving 55880 + -8142129x + 8086248x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8086248 the coefficient of the squared term: Divide each side by '8086248'. 0.006910497922 + -1.006910622x + x2 = 0 Move the constant term to the right: Add '-0.006910497922' to each side of the equation. 0.006910497922 + -1.006910622x + -0.006910497922 + x2 = 0 + -0.006910497922 Reorder the terms: 0.006910497922 + -0.006910497922 + -1.006910622x + x2 = 0 + -0.006910497922 Combine like terms: 0.006910497922 + -0.006910497922 = 0.000000000000 0.000000000000 + -1.006910622x + x2 = 0 + -0.006910497922 -1.006910622x + x2 = 0 + -0.006910497922 Combine like terms: 0 + -0.006910497922 = -0.006910497922 -1.006910622x + x2 = -0.006910497922 The x term is -1.006910622x. Take half its coefficient (-0.503455311). Square it (0.2534672502) and add it to both sides. Add '0.2534672502' to each side of the equation. -1.006910622x + 0.2534672502 + x2 = -0.006910497922 + 0.2534672502 Reorder the terms: 0.2534672502 + -1.006910622x + x2 = -0.006910497922 + 0.2534672502 Combine like terms: -0.006910497922 + 0.2534672502 = 0.246556752278 0.2534672502 + -1.006910622x + x2 = 0.246556752278 Factor a perfect square on the left side: (x + -0.503455311)(x + -0.503455311) = 0.246556752278 Calculate the square root of the right side: 0.496544814 Break this problem into two subproblems by setting (x + -0.503455311) equal to 0.496544814 and -0.496544814.Subproblem 1
x + -0.503455311 = 0.496544814 Simplifying x + -0.503455311 = 0.496544814 Reorder the terms: -0.503455311 + x = 0.496544814 Solving -0.503455311 + x = 0.496544814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.503455311' to each side of the equation. -0.503455311 + 0.503455311 + x = 0.496544814 + 0.503455311 Combine like terms: -0.503455311 + 0.503455311 = 0.000000000 0.000000000 + x = 0.496544814 + 0.503455311 x = 0.496544814 + 0.503455311 Combine like terms: 0.496544814 + 0.503455311 = 1.000000125 x = 1.000000125 Simplifying x = 1.000000125Subproblem 2
x + -0.503455311 = -0.496544814 Simplifying x + -0.503455311 = -0.496544814 Reorder the terms: -0.503455311 + x = -0.496544814 Solving -0.503455311 + x = -0.496544814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.503455311' to each side of the equation. -0.503455311 + 0.503455311 + x = -0.496544814 + 0.503455311 Combine like terms: -0.503455311 + 0.503455311 = 0.000000000 0.000000000 + x = -0.496544814 + 0.503455311 x = -0.496544814 + 0.503455311 Combine like terms: -0.496544814 + 0.503455311 = 0.006910497 x = 0.006910497 Simplifying x = 0.006910497Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.000000125, 0.006910497}
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