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Simplifying (2x + 0.3)(0.5x + 2) = 0 Reorder the terms: (0.3 + 2x)(0.5x + 2) = 0 Reorder the terms: (0.3 + 2x)(2 + 0.5x) = 0 Multiply (0.3 + 2x) * (2 + 0.5x) (0.3(2 + 0.5x) + 2x * (2 + 0.5x)) = 0 ((2 * 0.3 + 0.5x * 0.3) + 2x * (2 + 0.5x)) = 0 ((0.6 + 0.15x) + 2x * (2 + 0.5x)) = 0 (0.6 + 0.15x + (2 * 2x + 0.5x * 2x)) = 0 (0.6 + 0.15x + (4x + 1x2)) = 0 Combine like terms: 0.15x + 4x = 4.15x (0.6 + 4.15x + 1x2) = 0 Solving 0.6 + 4.15x + 1x2 = 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 + 4.15x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 4.15x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 4.15x + x2 = 0 + -0.6 4.15x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 4.15x + x2 = -0.6 The x term is 4.15x. Take half its coefficient (2.075). Square it (4.305625) and add it to both sides. Add '4.305625' to each side of the equation. 4.15x + 4.305625 + x2 = -0.6 + 4.305625 Reorder the terms: 4.305625 + 4.15x + x2 = -0.6 + 4.305625 Combine like terms: -0.6 + 4.305625 = 3.705625 4.305625 + 4.15x + x2 = 3.705625 Factor a perfect square on the left side: (x + 2.075)(x + 2.075) = 3.705625 Calculate the square root of the right side: 1.925 Break this problem into two subproblems by setting (x + 2.075) equal to 1.925 and -1.925.Subproblem 1
x + 2.075 = 1.925 Simplifying x + 2.075 = 1.925 Reorder the terms: 2.075 + x = 1.925 Solving 2.075 + x = 1.925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.075' to each side of the equation. 2.075 + -2.075 + x = 1.925 + -2.075 Combine like terms: 2.075 + -2.075 = 0.000 0.000 + x = 1.925 + -2.075 x = 1.925 + -2.075 Combine like terms: 1.925 + -2.075 = -0.15 x = -0.15 Simplifying x = -0.15Subproblem 2
x + 2.075 = -1.925 Simplifying x + 2.075 = -1.925 Reorder the terms: 2.075 + x = -1.925 Solving 2.075 + x = -1.925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.075' to each side of the equation. 2.075 + -2.075 + x = -1.925 + -2.075 Combine like terms: 2.075 + -2.075 = 0.000 0.000 + x = -1.925 + -2.075 x = -1.925 + -2.075 Combine like terms: -1.925 + -2.075 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.15, -4}
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