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Simplifying x(1 + -1x) + -0.02 = 0 (1 * x + -1x * x) + -0.02 = 0 (1x + -1x2) + -0.02 = 0 Reorder the terms: -0.02 + 1x + -1x2 = 0 Solving -0.02 + 1x + -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'. 0.02 + -1x + x2 = 0 Move the constant term to the right: Add '-0.02' to each side of the equation. 0.02 + -1x + -0.02 + x2 = 0 + -0.02 Reorder the terms: 0.02 + -0.02 + -1x + x2 = 0 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + -1x + x2 = 0 + -0.02 -1x + x2 = 0 + -0.02 Combine like terms: 0 + -0.02 = -0.02 -1x + x2 = -0.02 The x term is -1x. 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 = -0.02 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.02 + 0.25 Combine like terms: -0.02 + 0.25 = 0.23 0.25 + -1x + x2 = 0.23 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.23 Calculate the square root of the right side: 0.479583152 Break this problem into two subproblems by setting (x + -0.5) equal to 0.479583152 and -0.479583152.Subproblem 1
x + -0.5 = 0.479583152 Simplifying x + -0.5 = 0.479583152 Reorder the terms: -0.5 + x = 0.479583152 Solving -0.5 + x = 0.479583152 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 = 0.479583152 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.479583152 + 0.5 x = 0.479583152 + 0.5 Combine like terms: 0.479583152 + 0.5 = 0.979583152 x = 0.979583152 Simplifying x = 0.979583152Subproblem 2
x + -0.5 = -0.479583152 Simplifying x + -0.5 = -0.479583152 Reorder the terms: -0.5 + x = -0.479583152 Solving -0.5 + x = -0.479583152 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 = -0.479583152 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.479583152 + 0.5 x = -0.479583152 + 0.5 Combine like terms: -0.479583152 + 0.5 = 0.020416848 x = 0.020416848 Simplifying x = 0.020416848Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.979583152, 0.020416848}
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