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Simplifying (x + 0.2)(x + 3.3) = 0 Reorder the terms: (0.2 + x)(x + 3.3) = 0 Reorder the terms: (0.2 + x)(3.3 + x) = 0 Multiply (0.2 + x) * (3.3 + x) (0.2(3.3 + x) + x(3.3 + x)) = 0 ((3.3 * 0.2 + x * 0.2) + x(3.3 + x)) = 0 ((0.66 + 0.2x) + x(3.3 + x)) = 0 (0.66 + 0.2x + (3.3 * x + x * x)) = 0 (0.66 + 0.2x + (3.3x + x2)) = 0 Combine like terms: 0.2x + 3.3x = 3.5x (0.66 + 3.5x + x2) = 0 Solving 0.66 + 3.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.66' to each side of the equation. 0.66 + 3.5x + -0.66 + x2 = 0 + -0.66 Reorder the terms: 0.66 + -0.66 + 3.5x + x2 = 0 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + 3.5x + x2 = 0 + -0.66 3.5x + x2 = 0 + -0.66 Combine like terms: 0 + -0.66 = -0.66 3.5x + x2 = -0.66 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -0.66 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -0.66 + 3.0625 Combine like terms: -0.66 + 3.0625 = 2.4025 3.0625 + 3.5x + x2 = 2.4025 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 2.4025 Calculate the square root of the right side: 1.55 Break this problem into two subproblems by setting (x + 1.75) equal to 1.55 and -1.55.Subproblem 1
x + 1.75 = 1.55 Simplifying x + 1.75 = 1.55 Reorder the terms: 1.75 + x = 1.55 Solving 1.75 + x = 1.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.55 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.55 + -1.75 x = 1.55 + -1.75 Combine like terms: 1.55 + -1.75 = -0.2 x = -0.2 Simplifying x = -0.2Subproblem 2
x + 1.75 = -1.55 Simplifying x + 1.75 = -1.55 Reorder the terms: 1.75 + x = -1.55 Solving 1.75 + x = -1.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.55 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.55 + -1.75 x = -1.55 + -1.75 Combine like terms: -1.55 + -1.75 = -3.3 x = -3.3 Simplifying x = -3.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2, -3.3}
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