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Simplifying (0.03 + x)(0.8 + x) = 0 Multiply (0.03 + x) * (0.8 + x) (0.03(0.8 + x) + x(0.8 + x)) = 0 ((0.8 * 0.03 + x * 0.03) + x(0.8 + x)) = 0 ((0.024 + 0.03x) + x(0.8 + x)) = 0 (0.024 + 0.03x + (0.8 * x + x * x)) = 0 (0.024 + 0.03x + (0.8x + x2)) = 0 Combine like terms: 0.03x + 0.8x = 0.83x (0.024 + 0.83x + x2) = 0 Solving 0.024 + 0.83x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.024' to each side of the equation. 0.024 + 0.83x + -0.024 + x2 = 0 + -0.024 Reorder the terms: 0.024 + -0.024 + 0.83x + x2 = 0 + -0.024 Combine like terms: 0.024 + -0.024 = 0.000 0.000 + 0.83x + x2 = 0 + -0.024 0.83x + x2 = 0 + -0.024 Combine like terms: 0 + -0.024 = -0.024 0.83x + x2 = -0.024 The x term is 0.83x. Take half its coefficient (0.415). Square it (0.172225) and add it to both sides. Add '0.172225' to each side of the equation. 0.83x + 0.172225 + x2 = -0.024 + 0.172225 Reorder the terms: 0.172225 + 0.83x + x2 = -0.024 + 0.172225 Combine like terms: -0.024 + 0.172225 = 0.148225 0.172225 + 0.83x + x2 = 0.148225 Factor a perfect square on the left side: (x + 0.415)(x + 0.415) = 0.148225 Calculate the square root of the right side: 0.385 Break this problem into two subproblems by setting (x + 0.415) equal to 0.385 and -0.385.Subproblem 1
x + 0.415 = 0.385 Simplifying x + 0.415 = 0.385 Reorder the terms: 0.415 + x = 0.385 Solving 0.415 + x = 0.385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.415' to each side of the equation. 0.415 + -0.415 + x = 0.385 + -0.415 Combine like terms: 0.415 + -0.415 = 0.000 0.000 + x = 0.385 + -0.415 x = 0.385 + -0.415 Combine like terms: 0.385 + -0.415 = -0.03 x = -0.03 Simplifying x = -0.03Subproblem 2
x + 0.415 = -0.385 Simplifying x + 0.415 = -0.385 Reorder the terms: 0.415 + x = -0.385 Solving 0.415 + x = -0.385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.415' to each side of the equation. 0.415 + -0.415 + x = -0.385 + -0.415 Combine like terms: 0.415 + -0.415 = 0.000 0.000 + x = -0.385 + -0.415 x = -0.385 + -0.415 Combine like terms: -0.385 + -0.415 = -0.8 x = -0.8 Simplifying x = -0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.03, -0.8}
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