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Simplifying x2 + x + -254 = 0 Reorder the terms: -254 + x + x2 = 0 Solving -254 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '254' to each side of the equation. -254 + x + 254 + x2 = 0 + 254 Reorder the terms: -254 + 254 + x + x2 = 0 + 254 Combine like terms: -254 + 254 = 0 0 + x + x2 = 0 + 254 x + x2 = 0 + 254 Combine like terms: 0 + 254 = 254 x + x2 = 254 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 = 254 + 0.25 Reorder the terms: 0.25 + x + x2 = 254 + 0.25 Combine like terms: 254 + 0.25 = 254.25 0.25 + x + x2 = 254.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 254.25 Calculate the square root of the right side: 15.945218719 Break this problem into two subproblems by setting (x + 0.5) equal to 15.945218719 and -15.945218719.Subproblem 1
x + 0.5 = 15.945218719 Simplifying x + 0.5 = 15.945218719 Reorder the terms: 0.5 + x = 15.945218719 Solving 0.5 + x = 15.945218719 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 = 15.945218719 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 15.945218719 + -0.5 x = 15.945218719 + -0.5 Combine like terms: 15.945218719 + -0.5 = 15.445218719 x = 15.445218719 Simplifying x = 15.445218719Subproblem 2
x + 0.5 = -15.945218719 Simplifying x + 0.5 = -15.945218719 Reorder the terms: 0.5 + x = -15.945218719 Solving 0.5 + x = -15.945218719 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 = -15.945218719 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -15.945218719 + -0.5 x = -15.945218719 + -0.5 Combine like terms: -15.945218719 + -0.5 = -16.445218719 x = -16.445218719 Simplifying x = -16.445218719Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.445218719, -16.445218719}
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