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Simplifying x2 + -151x + 5000 = 0 Reorder the terms: 5000 + -151x + x2 = 0 Solving 5000 + -151x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -151x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -151x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -151x + x2 = 0 + -5000 -151x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -151x + x2 = -5000 The x term is -151x. Take half its coefficient (-75.5). Square it (5700.25) and add it to both sides. Add '5700.25' to each side of the equation. -151x + 5700.25 + x2 = -5000 + 5700.25 Reorder the terms: 5700.25 + -151x + x2 = -5000 + 5700.25 Combine like terms: -5000 + 5700.25 = 700.25 5700.25 + -151x + x2 = 700.25 Factor a perfect square on the left side: (x + -75.5)(x + -75.5) = 700.25 Calculate the square root of the right side: 26.462237245 Break this problem into two subproblems by setting (x + -75.5) equal to 26.462237245 and -26.462237245.Subproblem 1
x + -75.5 = 26.462237245 Simplifying x + -75.5 = 26.462237245 Reorder the terms: -75.5 + x = 26.462237245 Solving -75.5 + x = 26.462237245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75.5' to each side of the equation. -75.5 + 75.5 + x = 26.462237245 + 75.5 Combine like terms: -75.5 + 75.5 = 0.0 0.0 + x = 26.462237245 + 75.5 x = 26.462237245 + 75.5 Combine like terms: 26.462237245 + 75.5 = 101.962237245 x = 101.962237245 Simplifying x = 101.962237245Subproblem 2
x + -75.5 = -26.462237245 Simplifying x + -75.5 = -26.462237245 Reorder the terms: -75.5 + x = -26.462237245 Solving -75.5 + x = -26.462237245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75.5' to each side of the equation. -75.5 + 75.5 + x = -26.462237245 + 75.5 Combine like terms: -75.5 + 75.5 = 0.0 0.0 + x = -26.462237245 + 75.5 x = -26.462237245 + 75.5 Combine like terms: -26.462237245 + 75.5 = 49.037762755 x = 49.037762755 Simplifying x = 49.037762755Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.962237245, 49.037762755}
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