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Simplifying (0.100 + -1x)(0.200 + -1x) = 0 Multiply (0.100 + -1x) * (0.200 + -1x) (0.100(0.200 + -1x) + -1x * (0.200 + -1x)) = 0 ((0.200 * 0.100 + -1x * 0.100) + -1x * (0.200 + -1x)) = 0 ((0.02 + -0.1x) + -1x * (0.200 + -1x)) = 0 (0.02 + -0.1x + (0.200 * -1x + -1x * -1x)) = 0 (0.02 + -0.1x + (-0.2x + 1x2)) = 0 Combine like terms: -0.1x + -0.2x = -0.3x (0.02 + -0.3x + 1x2) = 0 Solving 0.02 + -0.3x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.02' to each side of the equation. 0.02 + -0.3x + -0.02 + x2 = 0 + -0.02 Reorder the terms: 0.02 + -0.02 + -0.3x + x2 = 0 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + -0.3x + x2 = 0 + -0.02 -0.3x + x2 = 0 + -0.02 Combine like terms: 0 + -0.02 = -0.02 -0.3x + x2 = -0.02 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = -0.02 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = -0.02 + 0.0225 Combine like terms: -0.02 + 0.0225 = 0.0025 0.0225 + -0.3x + x2 = 0.0025 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.0025 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + -0.15) equal to 0.05 and -0.05.Subproblem 1
x + -0.15 = 0.05 Simplifying x + -0.15 = 0.05 Reorder the terms: -0.15 + x = 0.05 Solving -0.15 + x = 0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 0.05 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.05 + 0.15 x = 0.05 + 0.15 Combine like terms: 0.05 + 0.15 = 0.2 x = 0.2 Simplifying x = 0.2Subproblem 2
x + -0.15 = -0.05 Simplifying x + -0.15 = -0.05 Reorder the terms: -0.15 + x = -0.05 Solving -0.15 + x = -0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -0.05 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.05 + 0.15 x = -0.05 + 0.15 Combine like terms: -0.05 + 0.15 = 0.1 x = 0.1 Simplifying x = 0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2, 0.1}
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