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Simplifying (x + 0.5)(x + 1.3) = 0 Reorder the terms: (0.5 + x)(x + 1.3) = 0 Reorder the terms: (0.5 + x)(1.3 + x) = 0 Multiply (0.5 + x) * (1.3 + x) (0.5(1.3 + x) + x(1.3 + x)) = 0 ((1.3 * 0.5 + x * 0.5) + x(1.3 + x)) = 0 ((0.65 + 0.5x) + x(1.3 + x)) = 0 (0.65 + 0.5x + (1.3 * x + x * x)) = 0 (0.65 + 0.5x + (1.3x + x2)) = 0 Combine like terms: 0.5x + 1.3x = 1.8x (0.65 + 1.8x + x2) = 0 Solving 0.65 + 1.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.65' to each side of the equation. 0.65 + 1.8x + -0.65 + x2 = 0 + -0.65 Reorder the terms: 0.65 + -0.65 + 1.8x + x2 = 0 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + 1.8x + x2 = 0 + -0.65 1.8x + x2 = 0 + -0.65 Combine like terms: 0 + -0.65 = -0.65 1.8x + x2 = -0.65 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = -0.65 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = -0.65 + 0.81 Combine like terms: -0.65 + 0.81 = 0.16 0.81 + 1.8x + x2 = 0.16 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + 0.9) equal to 0.4 and -0.4.Subproblem 1
x + 0.9 = 0.4 Simplifying x + 0.9 = 0.4 Reorder the terms: 0.9 + x = 0.4 Solving 0.9 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 0.4 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.4 + -0.9 x = 0.4 + -0.9 Combine like terms: 0.4 + -0.9 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 2
x + 0.9 = -0.4 Simplifying x + 0.9 = -0.4 Reorder the terms: 0.9 + x = -0.4 Solving 0.9 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -0.4 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.4 + -0.9 x = -0.4 + -0.9 Combine like terms: -0.4 + -0.9 = -1.3 x = -1.3 Simplifying x = -1.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5, -1.3}
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