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Simplifying 104000 = x(x + 111) Reorder the terms: 104000 = x(111 + x) 104000 = (111 * x + x * x) 104000 = (111x + x2) Solving 104000 = 111x + x2 Solving for variable 'x'. Reorder the terms: 104000 + -111x + -1x2 = 111x + -111x + x2 + -1x2 Combine like terms: 111x + -111x = 0 104000 + -111x + -1x2 = 0 + x2 + -1x2 104000 + -111x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 104000 + -111x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -104000 + 111x + x2 = 0 Move the constant term to the right: Add '104000' to each side of the equation. -104000 + 111x + 104000 + x2 = 0 + 104000 Reorder the terms: -104000 + 104000 + 111x + x2 = 0 + 104000 Combine like terms: -104000 + 104000 = 0 0 + 111x + x2 = 0 + 104000 111x + x2 = 0 + 104000 Combine like terms: 0 + 104000 = 104000 111x + x2 = 104000 The x term is 111x. Take half its coefficient (55.5). Square it (3080.25) and add it to both sides. Add '3080.25' to each side of the equation. 111x + 3080.25 + x2 = 104000 + 3080.25 Reorder the terms: 3080.25 + 111x + x2 = 104000 + 3080.25 Combine like terms: 104000 + 3080.25 = 107080.25 3080.25 + 111x + x2 = 107080.25 Factor a perfect square on the left side: (x + 55.5)(x + 55.5) = 107080.25 Calculate the square root of the right side: 327.231187389 Break this problem into two subproblems by setting (x + 55.5) equal to 327.231187389 and -327.231187389.Subproblem 1
x + 55.5 = 327.231187389 Simplifying x + 55.5 = 327.231187389 Reorder the terms: 55.5 + x = 327.231187389 Solving 55.5 + x = 327.231187389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55.5' to each side of the equation. 55.5 + -55.5 + x = 327.231187389 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + x = 327.231187389 + -55.5 x = 327.231187389 + -55.5 Combine like terms: 327.231187389 + -55.5 = 271.731187389 x = 271.731187389 Simplifying x = 271.731187389Subproblem 2
x + 55.5 = -327.231187389 Simplifying x + 55.5 = -327.231187389 Reorder the terms: 55.5 + x = -327.231187389 Solving 55.5 + x = -327.231187389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55.5' to each side of the equation. 55.5 + -55.5 + x = -327.231187389 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + x = -327.231187389 + -55.5 x = -327.231187389 + -55.5 Combine like terms: -327.231187389 + -55.5 = -382.731187389 x = -382.731187389 Simplifying x = -382.731187389Solution
The solution to the problem is based on the solutions from the subproblems. x = {271.731187389, -382.731187389}
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