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Simplifying x2 + x = 0.01937046 Reorder the terms: x + x2 = 0.01937046 Solving x + x2 = 0.01937046 Solving for variable 'x'. Reorder the terms: -0.01937046 + x + x2 = 0.01937046 + -0.01937046 Combine like terms: 0.01937046 + -0.01937046 = 0.00000000 -0.01937046 + x + x2 = 0.00000000 Begin completing the square. Move the constant term to the right: Add '0.01937046' to each side of the equation. -0.01937046 + x + 0.01937046 + x2 = 0.00000000 + 0.01937046 Reorder the terms: -0.01937046 + 0.01937046 + x + x2 = 0.00000000 + 0.01937046 Combine like terms: -0.01937046 + 0.01937046 = 0.00000000 0.00000000 + x + x2 = 0.00000000 + 0.01937046 x + x2 = 0.00000000 + 0.01937046 Combine like terms: 0.00000000 + 0.01937046 = 0.01937046 x + x2 = 0.01937046 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 = 0.01937046 + 0.25 Reorder the terms: 0.25 + x + x2 = 0.01937046 + 0.25 Combine like terms: 0.01937046 + 0.25 = 0.26937046 0.25 + x + x2 = 0.26937046 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.26937046 Calculate the square root of the right side: 0.519009114 Break this problem into two subproblems by setting (x + 0.5) equal to 0.519009114 and -0.519009114.Subproblem 1
x + 0.5 = 0.519009114 Simplifying x + 0.5 = 0.519009114 Reorder the terms: 0.5 + x = 0.519009114 Solving 0.5 + x = 0.519009114 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 = 0.519009114 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.519009114 + -0.5 x = 0.519009114 + -0.5 Combine like terms: 0.519009114 + -0.5 = 0.019009114 x = 0.019009114 Simplifying x = 0.019009114Subproblem 2
x + 0.5 = -0.519009114 Simplifying x + 0.5 = -0.519009114 Reorder the terms: 0.5 + x = -0.519009114 Solving 0.5 + x = -0.519009114 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 = -0.519009114 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.519009114 + -0.5 x = -0.519009114 + -0.5 Combine like terms: -0.519009114 + -0.5 = -1.019009114 x = -1.019009114 Simplifying x = -1.019009114Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.019009114, -1.019009114}
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