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Simplifying x(1 + -1x) = 0.2097 (1 * x + -1x * x) = 0.2097 (1x + -1x2) = 0.2097 Solving 1x + -1x2 = 0.2097 Solving for variable 'x'. Reorder the terms: -0.2097 + 1x + -1x2 = 0.2097 + -0.2097 Combine like terms: 0.2097 + -0.2097 = 0.0000 -0.2097 + 1x + -1x2 = 0.0000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.2097 + -1x + x2 = 0.0000 Move the constant term to the right: Add '-0.2097' to each side of the equation. 0.2097 + -1x + -0.2097 + x2 = 0.0000 + -0.2097 Reorder the terms: 0.2097 + -0.2097 + -1x + x2 = 0.0000 + -0.2097 Combine like terms: 0.2097 + -0.2097 = 0.0000 0.0000 + -1x + x2 = 0.0000 + -0.2097 -1x + x2 = 0.0000 + -0.2097 Combine like terms: 0.0000 + -0.2097 = -0.2097 -1x + x2 = -0.2097 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 = -0.2097 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.2097 + 0.25 Combine like terms: -0.2097 + 0.25 = 0.0403 0.25 + -1x + x2 = 0.0403 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0403 Calculate the square root of the right side: 0.200748599 Break this problem into two subproblems by setting (x + -0.5) equal to 0.200748599 and -0.200748599.Subproblem 1
x + -0.5 = 0.200748599 Simplifying x + -0.5 = 0.200748599 Reorder the terms: -0.5 + x = 0.200748599 Solving -0.5 + x = 0.200748599 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 = 0.200748599 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.200748599 + 0.5 x = 0.200748599 + 0.5 Combine like terms: 0.200748599 + 0.5 = 0.700748599 x = 0.700748599 Simplifying x = 0.700748599Subproblem 2
x + -0.5 = -0.200748599 Simplifying x + -0.5 = -0.200748599 Reorder the terms: -0.5 + x = -0.200748599 Solving -0.5 + x = -0.200748599 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 = -0.200748599 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.200748599 + 0.5 x = -0.200748599 + 0.5 Combine like terms: -0.200748599 + 0.5 = 0.299251401 x = 0.299251401 Simplifying x = 0.299251401Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.700748599, 0.299251401}
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