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Simplifying (0.1 + -1x)(0.1 + -1x) = 0 Multiply (0.1 + -1x) * (0.1 + -1x) (0.1(0.1 + -1x) + -1x * (0.1 + -1x)) = 0 ((0.1 * 0.1 + -1x * 0.1) + -1x * (0.1 + -1x)) = 0 ((0.01 + -0.1x) + -1x * (0.1 + -1x)) = 0 (0.01 + -0.1x + (0.1 * -1x + -1x * -1x)) = 0 (0.01 + -0.1x + (-0.1x + 1x2)) = 0 Combine like terms: -0.1x + -0.1x = -0.2x (0.01 + -0.2x + 1x2) = 0 Solving 0.01 + -0.2x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + -0.2x + -0.01 + x2 = 0 + -0.01 Reorder the terms: 0.01 + -0.01 + -0.2x + x2 = 0 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + -0.2x + x2 = 0 + -0.01 -0.2x + x2 = 0 + -0.01 Combine like terms: 0 + -0.01 = -0.01 -0.2x + x2 = -0.01 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = -0.01 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = -0.01 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.01 + -0.2x + x2 = 0.00 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -0.1) equal to 0.00 and 0.00.Subproblem 1
x + -0.1 = 0.00 Simplifying x + -0.1 = 0.00 Reorder the terms: -0.1 + x = 0.00 Solving -0.1 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.00 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.00 + 0.1 x = 0.00 + 0.1 Combine like terms: 0.00 + 0.1 = 0.1 x = 0.1 Simplifying x = 0.1Subproblem 2
x + -0.1 = 0.00 Simplifying x + -0.1 = 0.00 Reorder the terms: -0.1 + x = 0.00 Solving -0.1 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.00 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.00 + 0.1 x = 0.00 + 0.1 Combine like terms: 0.00 + 0.1 = 0.1 x = 0.1 Simplifying x = 0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1, 0.1}
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