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Simplifying (0.25x + -0.05)(x + -1) = 0 Reorder the terms: (-0.05 + 0.25x)(x + -1) = 0 Reorder the terms: (-0.05 + 0.25x)(-1 + x) = 0 Multiply (-0.05 + 0.25x) * (-1 + x) (-0.05(-1 + x) + 0.25x * (-1 + x)) = 0 ((-1 * -0.05 + x * -0.05) + 0.25x * (-1 + x)) = 0 ((0.05 + -0.05x) + 0.25x * (-1 + x)) = 0 (0.05 + -0.05x + (-1 * 0.25x + x * 0.25x)) = 0 (0.05 + -0.05x + (-0.25x + 0.25x2)) = 0 Combine like terms: -0.05x + -0.25x = -0.3x (0.05 + -0.3x + 0.25x2) = 0 Solving 0.05 + -0.3x + 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'. 0.2 + -1.2x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.2x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.2x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.2x + x2 = 0 + -0.2 -1.2x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.2x + x2 = -0.2 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.2 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.2 + 0.36 Combine like terms: -0.2 + 0.36 = 0.16 0.36 + -1.2x + x2 = 0.16 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + -0.6) equal to 0.4 and -0.4.Subproblem 1
x + -0.6 = 0.4 Simplifying x + -0.6 = 0.4 Reorder the terms: -0.6 + x = 0.4 Solving -0.6 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.4 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.4 + 0.6 x = 0.4 + 0.6 Combine like terms: 0.4 + 0.6 = 1 x = 1 Simplifying x = 1Subproblem 2
x + -0.6 = -0.4 Simplifying x + -0.6 = -0.4 Reorder the terms: -0.6 + x = -0.4 Solving -0.6 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.4 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.4 + 0.6 x = -0.4 + 0.6 Combine like terms: -0.4 + 0.6 = 0.2 x = 0.2 Simplifying x = 0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, 0.2}
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