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Simplifying (x + 5)(x + 2) = 26 Reorder the terms: (5 + x)(x + 2) = 26 Reorder the terms: (5 + x)(2 + x) = 26 Multiply (5 + x) * (2 + x) (5(2 + x) + x(2 + x)) = 26 ((2 * 5 + x * 5) + x(2 + x)) = 26 ((10 + 5x) + x(2 + x)) = 26 (10 + 5x + (2 * x + x * x)) = 26 (10 + 5x + (2x + x2)) = 26 Combine like terms: 5x + 2x = 7x (10 + 7x + x2) = 26 Solving 10 + 7x + x2 = 26 Solving for variable 'x'. Reorder the terms: 10 + -26 + 7x + x2 = 26 + -26 Combine like terms: 10 + -26 = -16 -16 + 7x + x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -16 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 7x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 7x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 7x + x2 = 0 + 16 7x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 7x + x2 = 16 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 16 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 16 + 12.25 Combine like terms: 16 + 12.25 = 28.25 12.25 + 7x + x2 = 28.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + 3.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + 3.5 = 5.315072906 Simplifying x + 3.5 = 5.315072906 Reorder the terms: 3.5 + x = 5.315072906 Solving 3.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.315072906 + -3.5 x = 5.315072906 + -3.5 Combine like terms: 5.315072906 + -3.5 = 1.815072906 x = 1.815072906 Simplifying x = 1.815072906Subproblem 2
x + 3.5 = -5.315072906 Simplifying x + 3.5 = -5.315072906 Reorder the terms: 3.5 + x = -5.315072906 Solving 3.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.315072906 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.315072906 + -3.5 x = -5.315072906 + -3.5 Combine like terms: -5.315072906 + -3.5 = -8.815072906 x = -8.815072906 Simplifying x = -8.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.815072906, -8.815072906}
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