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Simplifying (x + 0.01)(x + 0.33) = x Reorder the terms: (0.01 + x)(x + 0.33) = x Reorder the terms: (0.01 + x)(0.33 + x) = x Multiply (0.01 + x) * (0.33 + x) (0.01(0.33 + x) + x(0.33 + x)) = x ((0.33 * 0.01 + x * 0.01) + x(0.33 + x)) = x ((0.0033 + 0.01x) + x(0.33 + x)) = x (0.0033 + 0.01x + (0.33 * x + x * x)) = x (0.0033 + 0.01x + (0.33x + x2)) = x Combine like terms: 0.01x + 0.33x = 0.34x (0.0033 + 0.34x + x2) = x Solving 0.0033 + 0.34x + x2 = x Solving for variable 'x'. Reorder the terms: 0.0033 + 0.34x + -1x + x2 = x + -1x Combine like terms: 0.34x + -1x = -0.66x 0.0033 + -0.66x + x2 = x + -1x Combine like terms: x + -1x = 0 0.0033 + -0.66x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.0033' to each side of the equation. 0.0033 + -0.66x + -0.0033 + x2 = 0 + -0.0033 Reorder the terms: 0.0033 + -0.0033 + -0.66x + x2 = 0 + -0.0033 Combine like terms: 0.0033 + -0.0033 = 0.0000 0.0000 + -0.66x + x2 = 0 + -0.0033 -0.66x + x2 = 0 + -0.0033 Combine like terms: 0 + -0.0033 = -0.0033 -0.66x + x2 = -0.0033 The x term is -0.66x. Take half its coefficient (-0.33). Square it (0.1089) and add it to both sides. Add '0.1089' to each side of the equation. -0.66x + 0.1089 + x2 = -0.0033 + 0.1089 Reorder the terms: 0.1089 + -0.66x + x2 = -0.0033 + 0.1089 Combine like terms: -0.0033 + 0.1089 = 0.1056 0.1089 + -0.66x + x2 = 0.1056 Factor a perfect square on the left side: (x + -0.33)(x + -0.33) = 0.1056 Calculate the square root of the right side: 0.324961536 Break this problem into two subproblems by setting (x + -0.33) equal to 0.324961536 and -0.324961536.Subproblem 1
x + -0.33 = 0.324961536 Simplifying x + -0.33 = 0.324961536 Reorder the terms: -0.33 + x = 0.324961536 Solving -0.33 + x = 0.324961536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.33' to each side of the equation. -0.33 + 0.33 + x = 0.324961536 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + x = 0.324961536 + 0.33 x = 0.324961536 + 0.33 Combine like terms: 0.324961536 + 0.33 = 0.654961536 x = 0.654961536 Simplifying x = 0.654961536Subproblem 2
x + -0.33 = -0.324961536 Simplifying x + -0.33 = -0.324961536 Reorder the terms: -0.33 + x = -0.324961536 Solving -0.33 + x = -0.324961536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.33' to each side of the equation. -0.33 + 0.33 + x = -0.324961536 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + x = -0.324961536 + 0.33 x = -0.324961536 + 0.33 Combine like terms: -0.324961536 + 0.33 = 0.005038464 x = 0.005038464 Simplifying x = 0.005038464Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.654961536, 0.005038464}
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