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Simplifying (x + 0.9)(x + 1.1) = 0 Reorder the terms: (0.9 + x)(x + 1.1) = 0 Reorder the terms: (0.9 + x)(1.1 + x) = 0 Multiply (0.9 + x) * (1.1 + x) (0.9(1.1 + x) + x(1.1 + x)) = 0 ((1.1 * 0.9 + x * 0.9) + x(1.1 + x)) = 0 ((0.99 + 0.9x) + x(1.1 + x)) = 0 (0.99 + 0.9x + (1.1 * x + x * x)) = 0 (0.99 + 0.9x + (1.1x + x2)) = 0 Combine like terms: 0.9x + 1.1x = 2x (0.99 + 2x + x2) = 0 Solving 0.99 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.99' to each side of the equation. 0.99 + 2x + -0.99 + x2 = 0 + -0.99 Reorder the terms: 0.99 + -0.99 + 2x + x2 = 0 + -0.99 Combine like terms: 0.99 + -0.99 = 0.00 0.00 + 2x + x2 = 0 + -0.99 2x + x2 = 0 + -0.99 Combine like terms: 0 + -0.99 = -0.99 2x + x2 = -0.99 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 = -0.99 + 1 Reorder the terms: 1 + 2x + x2 = -0.99 + 1 Combine like terms: -0.99 + 1 = 0.01 1 + 2x + x2 = 0.01 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.01 Calculate the square root of the right side: 0.1 Break this problem into two subproblems by setting (x + 1) equal to 0.1 and -0.1.Subproblem 1
x + 1 = 0.1 Simplifying x + 1 = 0.1 Reorder the terms: 1 + x = 0.1 Solving 1 + x = 0.1 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 = 0.1 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.1 + -1 x = 0.1 + -1 Combine like terms: 0.1 + -1 = -0.9 x = -0.9 Simplifying x = -0.9Subproblem 2
x + 1 = -0.1 Simplifying x + 1 = -0.1 Reorder the terms: 1 + x = -0.1 Solving 1 + x = -0.1 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 = -0.1 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.1 + -1 x = -0.1 + -1 Combine like terms: -0.1 + -1 = -1.1 x = -1.1 Simplifying x = -1.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.9, -1.1}
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