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Simplifying x(1 + -1x) = 0.21 (1 * x + -1x * x) = 0.21 (1x + -1x2) = 0.21 Solving 1x + -1x2 = 0.21 Solving for variable 'x'. Reorder the terms: -0.21 + 1x + -1x2 = 0.21 + -0.21 Combine like terms: 0.21 + -0.21 = 0.00 -0.21 + 1x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.21 + -1x + x2 = 0.00 Move the constant term to the right: Add '-0.21' to each side of the equation. 0.21 + -1x + -0.21 + x2 = 0.00 + -0.21 Reorder the terms: 0.21 + -0.21 + -1x + x2 = 0.00 + -0.21 Combine like terms: 0.21 + -0.21 = 0.00 0.00 + -1x + x2 = 0.00 + -0.21 -1x + x2 = 0.00 + -0.21 Combine like terms: 0.00 + -0.21 = -0.21 -1x + x2 = -0.21 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 = -0.21 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.21 + 0.25 Combine like terms: -0.21 + 0.25 = 0.04 0.25 + -1x + x2 = 0.04 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.04 Calculate the square root of the right side: 0.2 Break this problem into two subproblems by setting (x + -0.5) equal to 0.2 and -0.2.Subproblem 1
x + -0.5 = 0.2 Simplifying x + -0.5 = 0.2 Reorder the terms: -0.5 + x = 0.2 Solving -0.5 + x = 0.2 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 = 0.2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.2 + 0.5 x = 0.2 + 0.5 Combine like terms: 0.2 + 0.5 = 0.7 x = 0.7 Simplifying x = 0.7Subproblem 2
x + -0.5 = -0.2 Simplifying x + -0.5 = -0.2 Reorder the terms: -0.5 + x = -0.2 Solving -0.5 + x = -0.2 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 = -0.2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.2 + 0.5 x = -0.2 + 0.5 Combine like terms: -0.2 + 0.5 = 0.3 x = 0.3 Simplifying x = 0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7, 0.3}
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