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Simplifying (x + 0.01)(x + 0.01) = 0 Reorder the terms: (0.01 + x)(x + 0.01) = 0 Reorder the terms: (0.01 + x)(0.01 + x) = 0 Multiply (0.01 + x) * (0.01 + x) (0.01(0.01 + x) + x(0.01 + x)) = 0 ((0.01 * 0.01 + x * 0.01) + x(0.01 + x)) = 0 ((0.0001 + 0.01x) + x(0.01 + x)) = 0 (0.0001 + 0.01x + (0.01 * x + x * x)) = 0 (0.0001 + 0.01x + (0.01x + x2)) = 0 Combine like terms: 0.01x + 0.01x = 0.02x (0.0001 + 0.02x + x2) = 0 Solving 0.0001 + 0.02x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0001' to each side of the equation. 0.0001 + 0.02x + -0.0001 + x2 = 0 + -0.0001 Reorder the terms: 0.0001 + -0.0001 + 0.02x + x2 = 0 + -0.0001 Combine like terms: 0.0001 + -0.0001 = 0.0000 0.0000 + 0.02x + x2 = 0 + -0.0001 0.02x + x2 = 0 + -0.0001 Combine like terms: 0 + -0.0001 = -0.0001 0.02x + x2 = -0.0001 The x term is 0.02x. Take half its coefficient (0.01). Square it (0.0001) and add it to both sides. Add '0.0001' to each side of the equation. 0.02x + 0.0001 + x2 = -0.0001 + 0.0001 Reorder the terms: 0.0001 + 0.02x + x2 = -0.0001 + 0.0001 Combine like terms: -0.0001 + 0.0001 = 0.0000 0.0001 + 0.02x + x2 = 0.0000 Factor a perfect square on the left side: (x + 0.01)(x + 0.01) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + 0.01) equal to 0.0000 and 0.0000.Subproblem 1
x + 0.01 = 0.0000 Simplifying x + 0.01 = 0.0000 Reorder the terms: 0.01 + x = 0.0000 Solving 0.01 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = 0.0000 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = 0.0000 + -0.01 x = 0.0000 + -0.01 Combine like terms: 0.0000 + -0.01 = -0.01 x = -0.01 Simplifying x = -0.01Subproblem 2
x + 0.01 = 0.0000 Simplifying x + 0.01 = 0.0000 Reorder the terms: 0.01 + x = 0.0000 Solving 0.01 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = 0.0000 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = 0.0000 + -0.01 x = 0.0000 + -0.01 Combine like terms: 0.0000 + -0.01 = -0.01 x = -0.01 Simplifying x = -0.01Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.01, -0.01}
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