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Simplifying x2 + x = 10029 Reorder the terms: x + x2 = 10029 Solving x + x2 = 10029 Solving for variable 'x'. Reorder the terms: -10029 + x + x2 = 10029 + -10029 Combine like terms: 10029 + -10029 = 0 -10029 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10029' to each side of the equation. -10029 + x + 10029 + x2 = 0 + 10029 Reorder the terms: -10029 + 10029 + x + x2 = 0 + 10029 Combine like terms: -10029 + 10029 = 0 0 + x + x2 = 0 + 10029 x + x2 = 0 + 10029 Combine like terms: 0 + 10029 = 10029 x + x2 = 10029 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 10029 + 0.25 Reorder the terms: 0.25 + x + x2 = 10029 + 0.25 Combine like terms: 10029 + 0.25 = 10029.25 0.25 + x + x2 = 10029.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 10029.25 Calculate the square root of the right side: 100.146143211 Break this problem into two subproblems by setting (x + 0.5) equal to 100.146143211 and -100.146143211.Subproblem 1
x + 0.5 = 100.146143211 Simplifying x + 0.5 = 100.146143211 Reorder the terms: 0.5 + x = 100.146143211 Solving 0.5 + x = 100.146143211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 100.146143211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 100.146143211 + -0.5 x = 100.146143211 + -0.5 Combine like terms: 100.146143211 + -0.5 = 99.646143211 x = 99.646143211 Simplifying x = 99.646143211Subproblem 2
x + 0.5 = -100.146143211 Simplifying x + 0.5 = -100.146143211 Reorder the terms: 0.5 + x = -100.146143211 Solving 0.5 + x = -100.146143211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -100.146143211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -100.146143211 + -0.5 x = -100.146143211 + -0.5 Combine like terms: -100.146143211 + -0.5 = -100.646143211 x = -100.646143211 Simplifying x = -100.646143211Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.646143211, -100.646143211}
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