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Simplifying x(x + 1) + -600 = 1 Reorder the terms: x(1 + x) + -600 = 1 (1 * x + x * x) + -600 = 1 (1x + x2) + -600 = 1 Reorder the terms: -600 + 1x + x2 = 1 Solving -600 + 1x + x2 = 1 Solving for variable 'x'. Reorder the terms: -600 + -1 + 1x + x2 = 1 + -1 Combine like terms: -600 + -1 = -601 -601 + 1x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -601 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '601' to each side of the equation. -601 + 1x + 601 + x2 = 0 + 601 Reorder the terms: -601 + 601 + 1x + x2 = 0 + 601 Combine like terms: -601 + 601 = 0 0 + 1x + x2 = 0 + 601 1x + x2 = 0 + 601 Combine like terms: 0 + 601 = 601 1x + x2 = 601 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 = 601 + 0.25 Reorder the terms: 0.25 + x + x2 = 601 + 0.25 Combine like terms: 601 + 0.25 = 601.25 0.25 + x + x2 = 601.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 601.25 Calculate the square root of the right side: 24.52039967 Break this problem into two subproblems by setting (x + 0.5) equal to 24.52039967 and -24.52039967.Subproblem 1
x + 0.5 = 24.52039967 Simplifying x + 0.5 = 24.52039967 Reorder the terms: 0.5 + x = 24.52039967 Solving 0.5 + x = 24.52039967 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 = 24.52039967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 24.52039967 + -0.5 x = 24.52039967 + -0.5 Combine like terms: 24.52039967 + -0.5 = 24.02039967 x = 24.02039967 Simplifying x = 24.02039967Subproblem 2
x + 0.5 = -24.52039967 Simplifying x + 0.5 = -24.52039967 Reorder the terms: 0.5 + x = -24.52039967 Solving 0.5 + x = -24.52039967 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 = -24.52039967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -24.52039967 + -0.5 x = -24.52039967 + -0.5 Combine like terms: -24.52039967 + -0.5 = -25.02039967 x = -25.02039967 Simplifying x = -25.02039967Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.02039967, -25.02039967}
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