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Simplifying x2 + x = 1500 Reorder the terms: x + x2 = 1500 Solving x + x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + x + x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1500' to each side of the equation. -1500 + x + 1500 + x2 = 0 + 1500 Reorder the terms: -1500 + 1500 + x + x2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + x + x2 = 0 + 1500 x + x2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 x + x2 = 1500 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 = 1500 + 0.25 Reorder the terms: 0.25 + x + x2 = 1500 + 0.25 Combine like terms: 1500 + 0.25 = 1500.25 0.25 + x + x2 = 1500.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1500.25 Calculate the square root of the right side: 38.733060814 Break this problem into two subproblems by setting (x + 0.5) equal to 38.733060814 and -38.733060814.Subproblem 1
x + 0.5 = 38.733060814 Simplifying x + 0.5 = 38.733060814 Reorder the terms: 0.5 + x = 38.733060814 Solving 0.5 + x = 38.733060814 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 = 38.733060814 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 38.733060814 + -0.5 x = 38.733060814 + -0.5 Combine like terms: 38.733060814 + -0.5 = 38.233060814 x = 38.233060814 Simplifying x = 38.233060814Subproblem 2
x + 0.5 = -38.733060814 Simplifying x + 0.5 = -38.733060814 Reorder the terms: 0.5 + x = -38.733060814 Solving 0.5 + x = -38.733060814 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 = -38.733060814 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -38.733060814 + -0.5 x = -38.733060814 + -0.5 Combine like terms: -38.733060814 + -0.5 = -39.233060814 x = -39.233060814 Simplifying x = -39.233060814Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.233060814, -39.233060814}
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