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Simplifying (x)(x) + 69(x) + -23456789 = 0 Multiply x * x x2 + 69(x) + -23456789 = 0 Reorder the terms: -23456789 + 69x + x2 = 0 Solving -23456789 + 69x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '23456789' to each side of the equation. -23456789 + 69x + 23456789 + x2 = 0 + 23456789 Reorder the terms: -23456789 + 23456789 + 69x + x2 = 0 + 23456789 Combine like terms: -23456789 + 23456789 = 0 0 + 69x + x2 = 0 + 23456789 69x + x2 = 0 + 23456789 Combine like terms: 0 + 23456789 = 23456789 69x + x2 = 23456789 The x term is 69x. Take half its coefficient (34.5). Square it (1190.25) and add it to both sides. Add '1190.25' to each side of the equation. 69x + 1190.25 + x2 = 23456789 + 1190.25 Reorder the terms: 1190.25 + 69x + x2 = 23456789 + 1190.25 Combine like terms: 23456789 + 1190.25 = 23457979.25 1190.25 + 69x + x2 = 23457979.25 Factor a perfect square on the left side: (x + 34.5)(x + 34.5) = 23457979.25 Calculate the square root of the right side: 4843.343808775 Break this problem into two subproblems by setting (x + 34.5) equal to 4843.343808775 and -4843.343808775.Subproblem 1
x + 34.5 = 4843.343808775 Simplifying x + 34.5 = 4843.343808775 Reorder the terms: 34.5 + x = 4843.343808775 Solving 34.5 + x = 4843.343808775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.5' to each side of the equation. 34.5 + -34.5 + x = 4843.343808775 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + x = 4843.343808775 + -34.5 x = 4843.343808775 + -34.5 Combine like terms: 4843.343808775 + -34.5 = 4808.843808775 x = 4808.843808775 Simplifying x = 4808.843808775Subproblem 2
x + 34.5 = -4843.343808775 Simplifying x + 34.5 = -4843.343808775 Reorder the terms: 34.5 + x = -4843.343808775 Solving 34.5 + x = -4843.343808775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.5' to each side of the equation. 34.5 + -34.5 + x = -4843.343808775 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + x = -4843.343808775 + -34.5 x = -4843.343808775 + -34.5 Combine like terms: -4843.343808775 + -34.5 = -4877.843808775 x = -4877.843808775 Simplifying x = -4877.843808775Solution
The solution to the problem is based on the solutions from the subproblems. x = {4808.843808775, -4877.843808775}
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