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Simplifying (x + 0.4)(x + 1.6) = 0 Reorder the terms: (0.4 + x)(x + 1.6) = 0 Reorder the terms: (0.4 + x)(1.6 + x) = 0 Multiply (0.4 + x) * (1.6 + x) (0.4(1.6 + x) + x(1.6 + x)) = 0 ((1.6 * 0.4 + x * 0.4) + x(1.6 + x)) = 0 ((0.64 + 0.4x) + x(1.6 + x)) = 0 (0.64 + 0.4x + (1.6 * x + x * x)) = 0 (0.64 + 0.4x + (1.6x + x2)) = 0 Combine like terms: 0.4x + 1.6x = 2x (0.64 + 2x + x2) = 0 Solving 0.64 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.64' to each side of the equation. 0.64 + 2x + -0.64 + x2 = 0 + -0.64 Reorder the terms: 0.64 + -0.64 + 2x + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + 2x + x2 = 0 + -0.64 2x + x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 2x + x2 = -0.64 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.64 + 1 Reorder the terms: 1 + 2x + x2 = -0.64 + 1 Combine like terms: -0.64 + 1 = 0.36 1 + 2x + x2 = 0.36 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.36 Calculate the square root of the right side: 0.6 Break this problem into two subproblems by setting (x + 1) equal to 0.6 and -0.6.Subproblem 1
x + 1 = 0.6 Simplifying x + 1 = 0.6 Reorder the terms: 1 + x = 0.6 Solving 1 + x = 0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.6 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.6 + -1 x = 0.6 + -1 Combine like terms: 0.6 + -1 = -0.4 x = -0.4 Simplifying x = -0.4Subproblem 2
x + 1 = -0.6 Simplifying x + 1 = -0.6 Reorder the terms: 1 + x = -0.6 Solving 1 + x = -0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.6 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.6 + -1 x = -0.6 + -1 Combine like terms: -0.6 + -1 = -1.6 x = -1.6 Simplifying x = -1.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.4, -1.6}
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