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Simplifying (1 + -1x)(0.2 + -1x) = 0 Multiply (1 + -1x) * (0.2 + -1x) (1(0.2 + -1x) + -1x * (0.2 + -1x)) = 0 ((0.2 * 1 + -1x * 1) + -1x * (0.2 + -1x)) = 0 ((0.2 + -1x) + -1x * (0.2 + -1x)) = 0 (0.2 + -1x + (0.2 * -1x + -1x * -1x)) = 0 (0.2 + -1x + (-0.2x + 1x2)) = 0 Combine like terms: -1x + -0.2x = -1.2x (0.2 + -1.2x + 1x2) = 0 Solving 0.2 + -1.2x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.2x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.2x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.2x + x2 = 0 + -0.2 -1.2x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.2x + x2 = -0.2 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.2 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.2 + 0.36 Combine like terms: -0.2 + 0.36 = 0.16 0.36 + -1.2x + x2 = 0.16 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + -0.6) equal to 0.4 and -0.4.Subproblem 1
x + -0.6 = 0.4 Simplifying x + -0.6 = 0.4 Reorder the terms: -0.6 + x = 0.4 Solving -0.6 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.4 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.4 + 0.6 x = 0.4 + 0.6 Combine like terms: 0.4 + 0.6 = 1 x = 1 Simplifying x = 1Subproblem 2
x + -0.6 = -0.4 Simplifying x + -0.6 = -0.4 Reorder the terms: -0.6 + x = -0.4 Solving -0.6 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.4 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.4 + 0.6 x = -0.4 + 0.6 Combine like terms: -0.4 + 0.6 = 0.2 x = 0.2 Simplifying x = 0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, 0.2}
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