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Simplifying x(x + 1) = 2409 Reorder the terms: x(1 + x) = 2409 (1 * x + x * x) = 2409 (1x + x2) = 2409 Solving 1x + x2 = 2409 Solving for variable 'x'. Reorder the terms: -2409 + 1x + x2 = 2409 + -2409 Combine like terms: 2409 + -2409 = 0 -2409 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2409' to each side of the equation. -2409 + 1x + 2409 + x2 = 0 + 2409 Reorder the terms: -2409 + 2409 + 1x + x2 = 0 + 2409 Combine like terms: -2409 + 2409 = 0 0 + 1x + x2 = 0 + 2409 1x + x2 = 0 + 2409 Combine like terms: 0 + 2409 = 2409 1x + x2 = 2409 The x term is 1x. 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 = 2409 + 0.25 Reorder the terms: 0.25 + x + x2 = 2409 + 0.25 Combine like terms: 2409 + 0.25 = 2409.25 0.25 + x + x2 = 2409.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2409.25 Calculate the square root of the right side: 49.084111482 Break this problem into two subproblems by setting (x + 0.5) equal to 49.084111482 and -49.084111482.Subproblem 1
x + 0.5 = 49.084111482 Simplifying x + 0.5 = 49.084111482 Reorder the terms: 0.5 + x = 49.084111482 Solving 0.5 + x = 49.084111482 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 = 49.084111482 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 49.084111482 + -0.5 x = 49.084111482 + -0.5 Combine like terms: 49.084111482 + -0.5 = 48.584111482 x = 48.584111482 Simplifying x = 48.584111482Subproblem 2
x + 0.5 = -49.084111482 Simplifying x + 0.5 = -49.084111482 Reorder the terms: 0.5 + x = -49.084111482 Solving 0.5 + x = -49.084111482 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 = -49.084111482 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -49.084111482 + -0.5 x = -49.084111482 + -0.5 Combine like terms: -49.084111482 + -0.5 = -49.584111482 x = -49.584111482 Simplifying x = -49.584111482Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.584111482, -49.584111482}
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