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Simplifying (x + 0.34)(x + 0.23) = 2 Reorder the terms: (0.34 + x)(x + 0.23) = 2 Reorder the terms: (0.34 + x)(0.23 + x) = 2 Multiply (0.34 + x) * (0.23 + x) (0.34(0.23 + x) + x(0.23 + x)) = 2 ((0.23 * 0.34 + x * 0.34) + x(0.23 + x)) = 2 ((0.0782 + 0.34x) + x(0.23 + x)) = 2 (0.0782 + 0.34x + (0.23 * x + x * x)) = 2 (0.0782 + 0.34x + (0.23x + x2)) = 2 Combine like terms: 0.34x + 0.23x = 0.57x (0.0782 + 0.57x + x2) = 2 Solving 0.0782 + 0.57x + x2 = 2 Solving for variable 'x'. Reorder the terms: 0.0782 + -2 + 0.57x + x2 = 2 + -2 Combine like terms: 0.0782 + -2 = -1.9218 -1.9218 + 0.57x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -1.9218 + 0.57x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1.9218' to each side of the equation. -1.9218 + 0.57x + 1.9218 + x2 = 0 + 1.9218 Reorder the terms: -1.9218 + 1.9218 + 0.57x + x2 = 0 + 1.9218 Combine like terms: -1.9218 + 1.9218 = 0.0000 0.0000 + 0.57x + x2 = 0 + 1.9218 0.57x + x2 = 0 + 1.9218 Combine like terms: 0 + 1.9218 = 1.9218 0.57x + x2 = 1.9218 The x term is 0.57x. Take half its coefficient (0.285). Square it (0.081225) and add it to both sides. Add '0.081225' to each side of the equation. 0.57x + 0.081225 + x2 = 1.9218 + 0.081225 Reorder the terms: 0.081225 + 0.57x + x2 = 1.9218 + 0.081225 Combine like terms: 1.9218 + 0.081225 = 2.003025 0.081225 + 0.57x + x2 = 2.003025 Factor a perfect square on the left side: (x + 0.285)(x + 0.285) = 2.003025 Calculate the square root of the right side: 1.415282657 Break this problem into two subproblems by setting (x + 0.285) equal to 1.415282657 and -1.415282657.Subproblem 1
x + 0.285 = 1.415282657 Simplifying x + 0.285 = 1.415282657 Reorder the terms: 0.285 + x = 1.415282657 Solving 0.285 + x = 1.415282657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.285' to each side of the equation. 0.285 + -0.285 + x = 1.415282657 + -0.285 Combine like terms: 0.285 + -0.285 = 0.000 0.000 + x = 1.415282657 + -0.285 x = 1.415282657 + -0.285 Combine like terms: 1.415282657 + -0.285 = 1.130282657 x = 1.130282657 Simplifying x = 1.130282657Subproblem 2
x + 0.285 = -1.415282657 Simplifying x + 0.285 = -1.415282657 Reorder the terms: 0.285 + x = -1.415282657 Solving 0.285 + x = -1.415282657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.285' to each side of the equation. 0.285 + -0.285 + x = -1.415282657 + -0.285 Combine like terms: 0.285 + -0.285 = 0.000 0.000 + x = -1.415282657 + -0.285 x = -1.415282657 + -0.285 Combine like terms: -1.415282657 + -0.285 = -1.700282657 x = -1.700282657 Simplifying x = -1.700282657Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.130282657, -1.700282657}
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