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Simplifying x2 + -607.66x + 92023.67 = 0 Reorder the terms: 92023.67 + -607.66x + x2 = 0 Solving 92023.67 + -607.66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-92023.67' to each side of the equation. 92023.67 + -607.66x + -92023.67 + x2 = 0 + -92023.67 Reorder the terms: 92023.67 + -92023.67 + -607.66x + x2 = 0 + -92023.67 Combine like terms: 92023.67 + -92023.67 = 0.00 0.00 + -607.66x + x2 = 0 + -92023.67 -607.66x + x2 = 0 + -92023.67 Combine like terms: 0 + -92023.67 = -92023.67 -607.66x + x2 = -92023.67 The x term is -607.66x. Take half its coefficient (-303.83). Square it (92312.6689) and add it to both sides. Add '92312.6689' to each side of the equation. -607.66x + 92312.6689 + x2 = -92023.67 + 92312.6689 Reorder the terms: 92312.6689 + -607.66x + x2 = -92023.67 + 92312.6689 Combine like terms: -92023.67 + 92312.6689 = 288.9989 92312.6689 + -607.66x + x2 = 288.9989 Factor a perfect square on the left side: (x + -303.83)(x + -303.83) = 288.9989 Calculate the square root of the right side: 16.999967647 Break this problem into two subproblems by setting (x + -303.83) equal to 16.999967647 and -16.999967647.Subproblem 1
x + -303.83 = 16.999967647 Simplifying x + -303.83 = 16.999967647 Reorder the terms: -303.83 + x = 16.999967647 Solving -303.83 + x = 16.999967647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '303.83' to each side of the equation. -303.83 + 303.83 + x = 16.999967647 + 303.83 Combine like terms: -303.83 + 303.83 = 0.00 0.00 + x = 16.999967647 + 303.83 x = 16.999967647 + 303.83 Combine like terms: 16.999967647 + 303.83 = 320.829967647 x = 320.829967647 Simplifying x = 320.829967647Subproblem 2
x + -303.83 = -16.999967647 Simplifying x + -303.83 = -16.999967647 Reorder the terms: -303.83 + x = -16.999967647 Solving -303.83 + x = -16.999967647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '303.83' to each side of the equation. -303.83 + 303.83 + x = -16.999967647 + 303.83 Combine like terms: -303.83 + 303.83 = 0.00 0.00 + x = -16.999967647 + 303.83 x = -16.999967647 + 303.83 Combine like terms: -16.999967647 + 303.83 = 286.830032353 x = 286.830032353 Simplifying x = 286.830032353Solution
The solution to the problem is based on the solutions from the subproblems. x = {320.829967647, 286.830032353}
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