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Simplifying (x + 0.8)(x + 1.1) = 0 Reorder the terms: (0.8 + x)(x + 1.1) = 0 Reorder the terms: (0.8 + x)(1.1 + x) = 0 Multiply (0.8 + x) * (1.1 + x) (0.8(1.1 + x) + x(1.1 + x)) = 0 ((1.1 * 0.8 + x * 0.8) + x(1.1 + x)) = 0 ((0.88 + 0.8x) + x(1.1 + x)) = 0 (0.88 + 0.8x + (1.1 * x + x * x)) = 0 (0.88 + 0.8x + (1.1x + x2)) = 0 Combine like terms: 0.8x + 1.1x = 1.9x (0.88 + 1.9x + x2) = 0 Solving 0.88 + 1.9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.88' to each side of the equation. 0.88 + 1.9x + -0.88 + x2 = 0 + -0.88 Reorder the terms: 0.88 + -0.88 + 1.9x + x2 = 0 + -0.88 Combine like terms: 0.88 + -0.88 = 0.00 0.00 + 1.9x + x2 = 0 + -0.88 1.9x + x2 = 0 + -0.88 Combine like terms: 0 + -0.88 = -0.88 1.9x + x2 = -0.88 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 = -0.88 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = -0.88 + 0.9025 Combine like terms: -0.88 + 0.9025 = 0.0225 0.9025 + 1.9x + x2 = 0.0225 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = 0.0225 Calculate the square root of the right side: 0.15 Break this problem into two subproblems by setting (x + 0.95) equal to 0.15 and -0.15.Subproblem 1
x + 0.95 = 0.15 Simplifying x + 0.95 = 0.15 Reorder the terms: 0.95 + x = 0.15 Solving 0.95 + x = 0.15 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 = 0.15 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 0.15 + -0.95 x = 0.15 + -0.95 Combine like terms: 0.15 + -0.95 = -0.8 x = -0.8 Simplifying x = -0.8Subproblem 2
x + 0.95 = -0.15 Simplifying x + 0.95 = -0.15 Reorder the terms: 0.95 + x = -0.15 Solving 0.95 + x = -0.15 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 = -0.15 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -0.15 + -0.95 x = -0.15 + -0.95 Combine like terms: -0.15 + -0.95 = -1.1 x = -1.1 Simplifying x = -1.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.8, -1.1}
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