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Simplifying 1x2 + 443.432625675216x + -39.671192 = 0 Reorder the terms: -39.671192 + 443.432625675216x + 1x2 = 0 Solving -39.671192 + 443.432625675216x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '39.671192' to each side of the equation. -39.671192 + 443.432625675216x + 39.671192 + x2 = 0 + 39.671192 Reorder the terms: -39.671192 + 39.671192 + 443.432625675216x + x2 = 0 + 39.671192 Combine like terms: -39.671192 + 39.671192 = 0.000000 0.000000 + 443.432625675216x + x2 = 0 + 39.671192 443.432625675216x + x2 = 0 + 39.671192 Combine like terms: 0 + 39.671192 = 39.671192 443.432625675216x + x2 = 39.671192 The x term is 443.432625675216x. Take half its coefficient (221.7163128). Square it (49158.12336) and add it to both sides. Add '49158.12336' to each side of the equation. 443.432625675216x + 49158.12336 + x2 = 39.671192 + 49158.12336 Reorder the terms: 49158.12336 + 443.432625675216x + x2 = 39.671192 + 49158.12336 Combine like terms: 39.671192 + 49158.12336 = 49197.794552 49158.12336 + 443.432625675216x + x2 = 49197.794552 Factor a perfect square on the left side: (x + 221.7163128)(x + 221.7163128) = 49197.794552 Calculate the square root of the right side: 221.805758609 Break this problem into two subproblems by setting (x + 221.7163128) equal to 221.805758609 and -221.805758609.Subproblem 1
x + 221.7163128 = 221.805758609 Simplifying x + 221.7163128 = 221.805758609 Reorder the terms: 221.7163128 + x = 221.805758609 Solving 221.7163128 + x = 221.805758609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-221.7163128' to each side of the equation. 221.7163128 + -221.7163128 + x = 221.805758609 + -221.7163128 Combine like terms: 221.7163128 + -221.7163128 = 0.0000000 0.0000000 + x = 221.805758609 + -221.7163128 x = 221.805758609 + -221.7163128 Combine like terms: 221.805758609 + -221.7163128 = 0.089445809 x = 0.089445809 Simplifying x = 0.089445809Subproblem 2
x + 221.7163128 = -221.805758609 Simplifying x + 221.7163128 = -221.805758609 Reorder the terms: 221.7163128 + x = -221.805758609 Solving 221.7163128 + x = -221.805758609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-221.7163128' to each side of the equation. 221.7163128 + -221.7163128 + x = -221.805758609 + -221.7163128 Combine like terms: 221.7163128 + -221.7163128 = 0.0000000 0.0000000 + x = -221.805758609 + -221.7163128 x = -221.805758609 + -221.7163128 Combine like terms: -221.805758609 + -221.7163128 = -443.522071409 x = -443.522071409 Simplifying x = -443.522071409Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.089445809, -443.522071409}
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