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Simplifying (x + 0.25)(x + 0.8) = 0 Reorder the terms: (0.25 + x)(x + 0.8) = 0 Reorder the terms: (0.25 + x)(0.8 + x) = 0 Multiply (0.25 + x) * (0.8 + x) (0.25(0.8 + x) + x(0.8 + x)) = 0 ((0.8 * 0.25 + x * 0.25) + x(0.8 + x)) = 0 ((0.2 + 0.25x) + x(0.8 + x)) = 0 (0.2 + 0.25x + (0.8 * x + x * x)) = 0 (0.2 + 0.25x + (0.8x + x2)) = 0 Combine like terms: 0.25x + 0.8x = 1.05x (0.2 + 1.05x + x2) = 0 Solving 0.2 + 1.05x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.05x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.05x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.05x + x2 = 0 + -0.2 1.05x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.05x + x2 = -0.2 The x term is 1.05x. Take half its coefficient (0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. 1.05x + 0.275625 + x2 = -0.2 + 0.275625 Reorder the terms: 0.275625 + 1.05x + x2 = -0.2 + 0.275625 Combine like terms: -0.2 + 0.275625 = 0.075625 0.275625 + 1.05x + x2 = 0.075625 Factor a perfect square on the left side: (x + 0.525)(x + 0.525) = 0.075625 Calculate the square root of the right side: 0.275 Break this problem into two subproblems by setting (x + 0.525) equal to 0.275 and -0.275.Subproblem 1
x + 0.525 = 0.275 Simplifying x + 0.525 = 0.275 Reorder the terms: 0.525 + x = 0.275 Solving 0.525 + x = 0.275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = 0.275 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = 0.275 + -0.525 x = 0.275 + -0.525 Combine like terms: 0.275 + -0.525 = -0.25 x = -0.25 Simplifying x = -0.25Subproblem 2
x + 0.525 = -0.275 Simplifying x + 0.525 = -0.275 Reorder the terms: 0.525 + x = -0.275 Solving 0.525 + x = -0.275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = -0.275 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = -0.275 + -0.525 x = -0.275 + -0.525 Combine like terms: -0.275 + -0.525 = -0.8 x = -0.8 Simplifying x = -0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.25, -0.8}
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