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Simplifying 0.0002818382931 = x + x2 Solving 0.0002818382931 = x + x2 Solving for variable 'x'. Reorder the terms: 0.0002818382931 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 0.0002818382931 + -1x + -1x2 = 0 + x2 + -1x2 0.0002818382931 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.0002818382931 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.0002818382931 + x + x2 = 0 Move the constant term to the right: Add '0.0002818382931' to each side of the equation. -0.0002818382931 + x + 0.0002818382931 + x2 = 0 + 0.0002818382931 Reorder the terms: -0.0002818382931 + 0.0002818382931 + x + x2 = 0 + 0.0002818382931 Combine like terms: -0.0002818382931 + 0.0002818382931 = 0.0000000000000 0.0000000000000 + x + x2 = 0 + 0.0002818382931 x + x2 = 0 + 0.0002818382931 Combine like terms: 0 + 0.0002818382931 = 0.0002818382931 x + x2 = 0.0002818382931 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. + 0.25 + x2 = 0.0002818382931 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.0002818382931 + 0.25 Combine like terms: 0.0002818382931 + 0.25 = 0.2502818382931 1.25 + x2 = 0.2502818382931 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.2502818382931 Calculate the square root of the right side: 0.500281759 Break this problem into two subproblems by setting (x + 0.5) equal to 0.500281759 and -0.500281759.Subproblem 1
x + 0.5 = 0.500281759 Simplifying x + 0.5 = 0.500281759 Reorder the terms: 0.5 + x = 0.500281759 Solving 0.5 + x = 0.500281759 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 = 0.500281759 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.500281759 + -0.5 x = 0.500281759 + -0.5 Combine like terms: 0.500281759 + -0.5 = 0.000281759 x = 0.000281759 Simplifying x = 0.000281759Subproblem 2
x + 0.5 = -0.500281759 Simplifying x + 0.5 = -0.500281759 Reorder the terms: 0.5 + x = -0.500281759 Solving 0.5 + x = -0.500281759 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 = -0.500281759 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.500281759 + -0.5 x = -0.500281759 + -0.5 Combine like terms: -0.500281759 + -0.5 = -1.000281759 x = -1.000281759 Simplifying x = -1.000281759Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000281759, -1.000281759}
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