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Simplifying (1 + -1x)(1 + -1x) = 0.01 Multiply (1 + -1x) * (1 + -1x) (1(1 + -1x) + -1x * (1 + -1x)) = 0.01 ((1 * 1 + -1x * 1) + -1x * (1 + -1x)) = 0.01 ((1 + -1x) + -1x * (1 + -1x)) = 0.01 (1 + -1x + (1 * -1x + -1x * -1x)) = 0.01 (1 + -1x + (-1x + 1x2)) = 0.01 Combine like terms: -1x + -1x = -2x (1 + -2x + 1x2) = 0.01 Solving 1 + -2x + 1x2 = 0.01 Solving for variable 'x'. Reorder the terms: 1 + -0.01 + -2x + 1x2 = 0.01 + -0.01 Combine like terms: 1 + -0.01 = 0.99 0.99 + -2x + 1x2 = 0.01 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.99 + -2x + 1x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-0.99' to each side of the equation. 0.99 + -2x + -0.99 + x2 = 0.00 + -0.99 Reorder the terms: 0.99 + -0.99 + -2x + x2 = 0.00 + -0.99 Combine like terms: 0.99 + -0.99 = 0.00 0.00 + -2x + x2 = 0.00 + -0.99 -2x + x2 = 0.00 + -0.99 Combine like terms: 0.00 + -0.99 = -0.99 -2x + x2 = -0.99 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.99 + 1 Reorder the terms: 1 + -2x + x2 = -0.99 + 1 Combine like terms: -0.99 + 1 = 0.01 1 + -2x + x2 = 0.01 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.01 Calculate the square root of the right side: 0.1 Break this problem into two subproblems by setting (x + -1) equal to 0.1 and -0.1.Subproblem 1
x + -1 = 0.1 Simplifying x + -1 = 0.1 Reorder the terms: -1 + x = 0.1 Solving -1 + x = 0.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.1 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.1 + 1 x = 0.1 + 1 Combine like terms: 0.1 + 1 = 1.1 x = 1.1 Simplifying x = 1.1Subproblem 2
x + -1 = -0.1 Simplifying x + -1 = -0.1 Reorder the terms: -1 + x = -0.1 Solving -1 + x = -0.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.1 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.1 + 1 x = -0.1 + 1 Combine like terms: -0.1 + 1 = 0.9 x = 0.9 Simplifying x = 0.9Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1, 0.9}
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