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Simplifying (x + 1)(x + 1) + -0.25 = 0 Reorder the terms: (1 + x)(x + 1) + -0.25 = 0 Reorder the terms: (1 + x)(1 + x) + -0.25 = 0 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x)) + -0.25 = 0 ((1 * 1 + x * 1) + x(1 + x)) + -0.25 = 0 ((1 + 1x) + x(1 + x)) + -0.25 = 0 (1 + 1x + (1 * x + x * x)) + -0.25 = 0 (1 + 1x + (1x + x2)) + -0.25 = 0 Combine like terms: 1x + 1x = 2x (1 + 2x + x2) + -0.25 = 0 Reorder the terms: 1 + -0.25 + 2x + x2 = 0 Combine like terms: 1 + -0.25 = 0.75 0.75 + 2x + x2 = 0 Solving 0.75 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 2x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 2x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 2x + x2 = 0 + -0.75 2x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 2x + x2 = -0.75 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 = -0.75 + 1 Reorder the terms: 1 + 2x + x2 = -0.75 + 1 Combine like terms: -0.75 + 1 = 0.25 1 + 2x + x2 = 0.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + 1) equal to 0.5 and -0.5.Subproblem 1
x + 1 = 0.5 Simplifying x + 1 = 0.5 Reorder the terms: 1 + x = 0.5 Solving 1 + x = 0.5 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 = 0.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.5 + -1 x = 0.5 + -1 Combine like terms: 0.5 + -1 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 2
x + 1 = -0.5 Simplifying x + 1 = -0.5 Reorder the terms: 1 + x = -0.5 Solving 1 + x = -0.5 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 = -0.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.5 + -1 x = -0.5 + -1 Combine like terms: -0.5 + -1 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5, -1.5}
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