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Simplifying x + -1x2 + -0.126 = 0 Reorder the terms: -0.126 + x + -1x2 = 0 Solving -0.126 + x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.126 + -1x + x2 = 0 Move the constant term to the right: Add '-0.126' to each side of the equation. 0.126 + -1x + -0.126 + x2 = 0 + -0.126 Reorder the terms: 0.126 + -0.126 + -1x + x2 = 0 + -0.126 Combine like terms: 0.126 + -0.126 = 0.000 0.000 + -1x + x2 = 0 + -0.126 -1x + x2 = 0 + -0.126 Combine like terms: 0 + -0.126 = -0.126 -1x + x2 = -0.126 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. -1x + 0.25 + x2 = -0.126 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.126 + 0.25 Combine like terms: -0.126 + 0.25 = 0.124 0.25 + -1x + x2 = 0.124 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.124 Calculate the square root of the right side: 0.352136337 Break this problem into two subproblems by setting (x + 0.5) equal to 0.352136337 and -0.352136337.Subproblem 1
x + 0.5 = 0.352136337 Simplifying x + 0.5 = 0.352136337 Reorder the terms: 0.5 + x = 0.352136337 Solving 0.5 + x = 0.352136337 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 = 0.352136337 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.352136337 + -0.5 x = 0.352136337 + -0.5 Combine like terms: 0.352136337 + -0.5 = -0.147863663 x = -0.147863663 Simplifying x = -0.147863663Subproblem 2
x + 0.5 = -0.352136337 Simplifying x + 0.5 = -0.352136337 Reorder the terms: 0.5 + x = -0.352136337 Solving 0.5 + x = -0.352136337 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 = -0.352136337 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.352136337 + -0.5 x = -0.352136337 + -0.5 Combine like terms: -0.352136337 + -0.5 = -0.852136337 x = -0.852136337 Simplifying x = -0.852136337Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.147863663, -0.852136337}
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