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Simplifying (x + 0.8)(x + 2.5) = 0 Reorder the terms: (0.8 + x)(x + 2.5) = 0 Reorder the terms: (0.8 + x)(2.5 + x) = 0 Multiply (0.8 + x) * (2.5 + x) (0.8(2.5 + x) + x(2.5 + x)) = 0 ((2.5 * 0.8 + x * 0.8) + x(2.5 + x)) = 0 ((2 + 0.8x) + x(2.5 + x)) = 0 (2 + 0.8x + (2.5 * x + x * x)) = 0 (2 + 0.8x + (2.5x + x2)) = 0 Combine like terms: 0.8x + 2.5x = 3.3x (2 + 3.3x + x2) = 0 Solving 2 + 3.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.3x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.3x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.3x + x2 = 0 + -2 3.3x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.3x + x2 = -2 The x term is 3.3x. Take half its coefficient (1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. 3.3x + 2.7225 + x2 = -2 + 2.7225 Reorder the terms: 2.7225 + 3.3x + x2 = -2 + 2.7225 Combine like terms: -2 + 2.7225 = 0.7225 2.7225 + 3.3x + x2 = 0.7225 Factor a perfect square on the left side: (x + 1.65)(x + 1.65) = 0.7225 Calculate the square root of the right side: 0.85 Break this problem into two subproblems by setting (x + 1.65) equal to 0.85 and -0.85.Subproblem 1
x + 1.65 = 0.85 Simplifying x + 1.65 = 0.85 Reorder the terms: 1.65 + x = 0.85 Solving 1.65 + x = 0.85 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + x = 0.85 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + x = 0.85 + -1.65 x = 0.85 + -1.65 Combine like terms: 0.85 + -1.65 = -0.8 x = -0.8 Simplifying x = -0.8Subproblem 2
x + 1.65 = -0.85 Simplifying x + 1.65 = -0.85 Reorder the terms: 1.65 + x = -0.85 Solving 1.65 + x = -0.85 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + x = -0.85 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + x = -0.85 + -1.65 x = -0.85 + -1.65 Combine like terms: -0.85 + -1.65 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.8, -2.5}
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