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Simplifying x(1 + -1x) = 0.04 (1 * x + -1x * x) = 0.04 (1x + -1x2) = 0.04 Solving 1x + -1x2 = 0.04 Solving for variable 'x'. Reorder the terms: -0.04 + 1x + -1x2 = 0.04 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 -0.04 + 1x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.04 + -1x + x2 = 0.00 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + -1x + -0.04 + x2 = 0.00 + -0.04 Reorder the terms: 0.04 + -0.04 + -1x + x2 = 0.00 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + -1x + x2 = 0.00 + -0.04 -1x + x2 = 0.00 + -0.04 Combine like terms: 0.00 + -0.04 = -0.04 -1x + x2 = -0.04 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 = -0.04 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.04 + 0.25 Combine like terms: -0.04 + 0.25 = 0.21 0.25 + -1x + x2 = 0.21 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (x + -0.5) equal to 0.458257569 and -0.458257569.Subproblem 1
x + -0.5 = 0.458257569 Simplifying x + -0.5 = 0.458257569 Reorder the terms: -0.5 + x = 0.458257569 Solving -0.5 + x = 0.458257569 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 = 0.458257569 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.458257569 + 0.5 x = 0.458257569 + 0.5 Combine like terms: 0.458257569 + 0.5 = 0.958257569 x = 0.958257569 Simplifying x = 0.958257569Subproblem 2
x + -0.5 = -0.458257569 Simplifying x + -0.5 = -0.458257569 Reorder the terms: -0.5 + x = -0.458257569 Solving -0.5 + x = -0.458257569 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 = -0.458257569 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.458257569 + 0.5 x = -0.458257569 + 0.5 Combine like terms: -0.458257569 + 0.5 = 0.041742431 x = 0.041742431 Simplifying x = 0.041742431Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.958257569, 0.041742431}
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