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Simplifying x2 + 52000x + -25919.5 = 0 Reorder the terms: -25919.5 + 52000x + x2 = 0 Solving -25919.5 + 52000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25919.5' to each side of the equation. -25919.5 + 52000x + 25919.5 + x2 = 0 + 25919.5 Reorder the terms: -25919.5 + 25919.5 + 52000x + x2 = 0 + 25919.5 Combine like terms: -25919.5 + 25919.5 = 0.0 0.0 + 52000x + x2 = 0 + 25919.5 52000x + x2 = 0 + 25919.5 Combine like terms: 0 + 25919.5 = 25919.5 52000x + x2 = 25919.5 The x term is 52000x. Take half its coefficient (26000). Square it (676000000) and add it to both sides. Add '676000000' to each side of the equation. 52000x + 676000000 + x2 = 25919.5 + 676000000 Reorder the terms: 676000000 + 52000x + x2 = 25919.5 + 676000000 Combine like terms: 25919.5 + 676000000 = 676025919.5 676000000 + 52000x + x2 = 676025919.5 Factor a perfect square on the left side: (x + 26000)(x + 26000) = 676025919.5 Calculate the square root of the right side: 26000.498447145 Break this problem into two subproblems by setting (x + 26000) equal to 26000.498447145 and -26000.498447145.Subproblem 1
x + 26000 = 26000.498447145 Simplifying x + 26000 = 26000.498447145 Reorder the terms: 26000 + x = 26000.498447145 Solving 26000 + x = 26000.498447145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26000' to each side of the equation. 26000 + -26000 + x = 26000.498447145 + -26000 Combine like terms: 26000 + -26000 = 0 0 + x = 26000.498447145 + -26000 x = 26000.498447145 + -26000 Combine like terms: 26000.498447145 + -26000 = 0.498447145 x = 0.498447145 Simplifying x = 0.498447145Subproblem 2
x + 26000 = -26000.498447145 Simplifying x + 26000 = -26000.498447145 Reorder the terms: 26000 + x = -26000.498447145 Solving 26000 + x = -26000.498447145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26000' to each side of the equation. 26000 + -26000 + x = -26000.498447145 + -26000 Combine like terms: 26000 + -26000 = 0 0 + x = -26000.498447145 + -26000 x = -26000.498447145 + -26000 Combine like terms: -26000.498447145 + -26000 = -52000.498447145 x = -52000.498447145 Simplifying x = -52000.498447145Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.498447145, -52000.498447145}
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