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Simplifying (x + -2)(x + -1) = 28 Reorder the terms: (-2 + x)(x + -1) = 28 Reorder the terms: (-2 + x)(-1 + x) = 28 Multiply (-2 + x) * (-1 + x) (-2(-1 + x) + x(-1 + x)) = 28 ((-1 * -2 + x * -2) + x(-1 + x)) = 28 ((2 + -2x) + x(-1 + x)) = 28 (2 + -2x + (-1 * x + x * x)) = 28 (2 + -2x + (-1x + x2)) = 28 Combine like terms: -2x + -1x = -3x (2 + -3x + x2) = 28 Solving 2 + -3x + x2 = 28 Solving for variable 'x'. Reorder the terms: 2 + -28 + -3x + x2 = 28 + -28 Combine like terms: 2 + -28 = -26 -26 + -3x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -26 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -3x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -3x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -3x + x2 = 0 + 26 -3x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -3x + x2 = 26 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 26 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 26 + 2.25 Combine like terms: 26 + 2.25 = 28.25 2.25 + -3x + x2 = 28.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -1.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + -1.5 = 5.315072906 Simplifying x + -1.5 = 5.315072906 Reorder the terms: -1.5 + x = 5.315072906 Solving -1.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.315072906 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.315072906 + 1.5 x = 5.315072906 + 1.5 Combine like terms: 5.315072906 + 1.5 = 6.815072906 x = 6.815072906 Simplifying x = 6.815072906Subproblem 2
x + -1.5 = -5.315072906 Simplifying x + -1.5 = -5.315072906 Reorder the terms: -1.5 + x = -5.315072906 Solving -1.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.315072906 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.315072906 + 1.5 x = -5.315072906 + 1.5 Combine like terms: -5.315072906 + 1.5 = -3.815072906 x = -3.815072906 Simplifying x = -3.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.815072906, -3.815072906}
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