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Simplifying (0.5x + 0.1)(0.5x + 0.1) = 0 Reorder the terms: (0.1 + 0.5x)(0.5x + 0.1) = 0 Reorder the terms: (0.1 + 0.5x)(0.1 + 0.5x) = 0 Multiply (0.1 + 0.5x) * (0.1 + 0.5x) (0.1(0.1 + 0.5x) + 0.5x * (0.1 + 0.5x)) = 0 ((0.1 * 0.1 + 0.5x * 0.1) + 0.5x * (0.1 + 0.5x)) = 0 ((0.01 + 0.05x) + 0.5x * (0.1 + 0.5x)) = 0 (0.01 + 0.05x + (0.1 * 0.5x + 0.5x * 0.5x)) = 0 (0.01 + 0.05x + (0.05x + 0.25x2)) = 0 Combine like terms: 0.05x + 0.05x = 0.1x (0.01 + 0.1x + 0.25x2) = 0 Solving 0.01 + 0.1x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 0.04 + 0.4x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 0.4x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 0.4x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 0.4x + x2 = 0 + -0.04 0.4x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 0.4x + x2 = -0.04 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = -0.04 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = -0.04 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.04 + 0.4x + x2 = 0.00 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 0.2) equal to 0.00 and 0.00.Subproblem 1
x + 0.2 = 0.00 Simplifying x + 0.2 = 0.00 Reorder the terms: 0.2 + x = 0.00 Solving 0.2 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.00 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.00 + -0.2 x = 0.00 + -0.2 Combine like terms: 0.00 + -0.2 = -0.2 x = -0.2 Simplifying x = -0.2Subproblem 2
x + 0.2 = 0.00 Simplifying x + 0.2 = 0.00 Reorder the terms: 0.2 + x = 0.00 Solving 0.2 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.00 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.00 + -0.2 x = 0.00 + -0.2 Combine like terms: 0.00 + -0.2 = -0.2 x = -0.2 Simplifying x = -0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2, -0.2}
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