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Simplifying x2 + x = 435600 Reorder the terms: x + x2 = 435600 Solving x + x2 = 435600 Solving for variable 'x'. Reorder the terms: -435600 + x + x2 = 435600 + -435600 Combine like terms: 435600 + -435600 = 0 -435600 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '435600' to each side of the equation. -435600 + x + 435600 + x2 = 0 + 435600 Reorder the terms: -435600 + 435600 + x + x2 = 0 + 435600 Combine like terms: -435600 + 435600 = 0 0 + x + x2 = 0 + 435600 x + x2 = 0 + 435600 Combine like terms: 0 + 435600 = 435600 x + x2 = 435600 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 = 435600 + 0.25 Reorder the terms: 0.25 + x + x2 = 435600 + 0.25 Combine like terms: 435600 + 0.25 = 435600.25 0.25 + x + x2 = 435600.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 435600.25 Calculate the square root of the right side: 660.000189394 Break this problem into two subproblems by setting (x + 0.5) equal to 660.000189394 and -660.000189394.Subproblem 1
x + 0.5 = 660.000189394 Simplifying x + 0.5 = 660.000189394 Reorder the terms: 0.5 + x = 660.000189394 Solving 0.5 + x = 660.000189394 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 = 660.000189394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 660.000189394 + -0.5 x = 660.000189394 + -0.5 Combine like terms: 660.000189394 + -0.5 = 659.500189394 x = 659.500189394 Simplifying x = 659.500189394Subproblem 2
x + 0.5 = -660.000189394 Simplifying x + 0.5 = -660.000189394 Reorder the terms: 0.5 + x = -660.000189394 Solving 0.5 + x = -660.000189394 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 = -660.000189394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -660.000189394 + -0.5 x = -660.000189394 + -0.5 Combine like terms: -660.000189394 + -0.5 = -660.500189394 x = -660.500189394 Simplifying x = -660.500189394Solution
The solution to the problem is based on the solutions from the subproblems. x = {659.500189394, -660.500189394}
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