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Simplifying (x + 0.2)(x + 4.3) = 0 Reorder the terms: (0.2 + x)(x + 4.3) = 0 Reorder the terms: (0.2 + x)(4.3 + x) = 0 Multiply (0.2 + x) * (4.3 + x) (0.2(4.3 + x) + x(4.3 + x)) = 0 ((4.3 * 0.2 + x * 0.2) + x(4.3 + x)) = 0 ((0.86 + 0.2x) + x(4.3 + x)) = 0 (0.86 + 0.2x + (4.3 * x + x * x)) = 0 (0.86 + 0.2x + (4.3x + x2)) = 0 Combine like terms: 0.2x + 4.3x = 4.5x (0.86 + 4.5x + x2) = 0 Solving 0.86 + 4.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.86' to each side of the equation. 0.86 + 4.5x + -0.86 + x2 = 0 + -0.86 Reorder the terms: 0.86 + -0.86 + 4.5x + x2 = 0 + -0.86 Combine like terms: 0.86 + -0.86 = 0.00 0.00 + 4.5x + x2 = 0 + -0.86 4.5x + x2 = 0 + -0.86 Combine like terms: 0 + -0.86 = -0.86 4.5x + x2 = -0.86 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -0.86 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -0.86 + 5.0625 Combine like terms: -0.86 + 5.0625 = 4.2025 5.0625 + 4.5x + x2 = 4.2025 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 4.2025 Calculate the square root of the right side: 2.05 Break this problem into two subproblems by setting (x + 2.25) equal to 2.05 and -2.05.Subproblem 1
x + 2.25 = 2.05 Simplifying x + 2.25 = 2.05 Reorder the terms: 2.25 + x = 2.05 Solving 2.25 + x = 2.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.05 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.05 + -2.25 x = 2.05 + -2.25 Combine like terms: 2.05 + -2.25 = -0.2 x = -0.2 Simplifying x = -0.2Subproblem 2
x + 2.25 = -2.05 Simplifying x + 2.25 = -2.05 Reorder the terms: 2.25 + x = -2.05 Solving 2.25 + x = -2.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.05 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.05 + -2.25 x = -2.05 + -2.25 Combine like terms: -2.05 + -2.25 = -4.3 x = -4.3 Simplifying x = -4.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2, -4.3}
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