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Simplifying x2 + x + -125000 = 0 Reorder the terms: -125000 + x + x2 = 0 Solving -125000 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '125000' to each side of the equation. -125000 + x + 125000 + x2 = 0 + 125000 Reorder the terms: -125000 + 125000 + x + x2 = 0 + 125000 Combine like terms: -125000 + 125000 = 0 0 + x + x2 = 0 + 125000 x + x2 = 0 + 125000 Combine like terms: 0 + 125000 = 125000 x + x2 = 125000 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 = 125000 + 0.25 Reorder the terms: 0.25 + x + x2 = 125000 + 0.25 Combine like terms: 125000 + 0.25 = 125000.25 0.25 + x + x2 = 125000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 125000.25 Calculate the square root of the right side: 353.553744146 Break this problem into two subproblems by setting (x + 0.5) equal to 353.553744146 and -353.553744146.Subproblem 1
x + 0.5 = 353.553744146 Simplifying x + 0.5 = 353.553744146 Reorder the terms: 0.5 + x = 353.553744146 Solving 0.5 + x = 353.553744146 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 = 353.553744146 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 353.553744146 + -0.5 x = 353.553744146 + -0.5 Combine like terms: 353.553744146 + -0.5 = 353.053744146 x = 353.053744146 Simplifying x = 353.053744146Subproblem 2
x + 0.5 = -353.553744146 Simplifying x + 0.5 = -353.553744146 Reorder the terms: 0.5 + x = -353.553744146 Solving 0.5 + x = -353.553744146 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 = -353.553744146 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -353.553744146 + -0.5 x = -353.553744146 + -0.5 Combine like terms: -353.553744146 + -0.5 = -354.053744146 x = -354.053744146 Simplifying x = -354.053744146Solution
The solution to the problem is based on the solutions from the subproblems. x = {353.053744146, -354.053744146}
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