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Simplifying x2 + x + -128 = 0 Reorder the terms: -128 + x + x2 = 0 Solving -128 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + x + x2 = 0 + 128 x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 x + x2 = 128 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 = 128 + 0.25 Reorder the terms: 0.25 + x + x2 = 128 + 0.25 Combine like terms: 128 + 0.25 = 128.25 0.25 + x + x2 = 128.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + 0.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + 0.5 = 11.324751653 Simplifying x + 0.5 = 11.324751653 Reorder the terms: 0.5 + x = 11.324751653 Solving 0.5 + x = 11.324751653 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 = 11.324751653 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.324751653 + -0.5 x = 11.324751653 + -0.5 Combine like terms: 11.324751653 + -0.5 = 10.824751653 x = 10.824751653 Simplifying x = 10.824751653Subproblem 2
x + 0.5 = -11.324751653 Simplifying x + 0.5 = -11.324751653 Reorder the terms: 0.5 + x = -11.324751653 Solving 0.5 + x = -11.324751653 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 = -11.324751653 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.324751653 + -0.5 x = -11.324751653 + -0.5 Combine like terms: -11.324751653 + -0.5 = -11.824751653 x = -11.824751653 Simplifying x = -11.824751653Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.824751653, -11.824751653}
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