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Simplifying (x + 0.4)(x + 1.5) = 0 Reorder the terms: (0.4 + x)(x + 1.5) = 0 Reorder the terms: (0.4 + x)(1.5 + x) = 0 Multiply (0.4 + x) * (1.5 + x) (0.4(1.5 + x) + x(1.5 + x)) = 0 ((1.5 * 0.4 + x * 0.4) + x(1.5 + x)) = 0 ((0.6 + 0.4x) + x(1.5 + x)) = 0 (0.6 + 0.4x + (1.5 * x + x * x)) = 0 (0.6 + 0.4x + (1.5x + x2)) = 0 Combine like terms: 0.4x + 1.5x = 1.9x (0.6 + 1.9x + x2) = 0 Solving 0.6 + 1.9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 1.9x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 1.9x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 1.9x + x2 = 0 + -0.6 1.9x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 1.9x + x2 = -0.6 The x term is 1.9x. Take half its coefficient (0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. 1.9x + 0.9025 + x2 = -0.6 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = -0.6 + 0.9025 Combine like terms: -0.6 + 0.9025 = 0.3025 0.9025 + 1.9x + x2 = 0.3025 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = 0.3025 Calculate the square root of the right side: 0.55 Break this problem into two subproblems by setting (x + 0.95) equal to 0.55 and -0.55.Subproblem 1
x + 0.95 = 0.55 Simplifying x + 0.95 = 0.55 Reorder the terms: 0.95 + x = 0.55 Solving 0.95 + x = 0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = 0.55 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 0.55 + -0.95 x = 0.55 + -0.95 Combine like terms: 0.55 + -0.95 = -0.4 x = -0.4 Simplifying x = -0.4Subproblem 2
x + 0.95 = -0.55 Simplifying x + 0.95 = -0.55 Reorder the terms: 0.95 + x = -0.55 Solving 0.95 + x = -0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = -0.55 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -0.55 + -0.95 x = -0.55 + -0.95 Combine like terms: -0.55 + -0.95 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.4, -1.5}
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