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Simplifying (x + 13)(x + 5) + 2 = 0 Reorder the terms: (13 + x)(x + 5) + 2 = 0 Reorder the terms: (13 + x)(5 + x) + 2 = 0 Multiply (13 + x) * (5 + x) (13(5 + x) + x(5 + x)) + 2 = 0 ((5 * 13 + x * 13) + x(5 + x)) + 2 = 0 ((65 + 13x) + x(5 + x)) + 2 = 0 (65 + 13x + (5 * x + x * x)) + 2 = 0 (65 + 13x + (5x + x2)) + 2 = 0 Combine like terms: 13x + 5x = 18x (65 + 18x + x2) + 2 = 0 Reorder the terms: 65 + 2 + 18x + x2 = 0 Combine like terms: 65 + 2 = 67 67 + 18x + x2 = 0 Solving 67 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-67' to each side of the equation. 67 + 18x + -67 + x2 = 0 + -67 Reorder the terms: 67 + -67 + 18x + x2 = 0 + -67 Combine like terms: 67 + -67 = 0 0 + 18x + x2 = 0 + -67 18x + x2 = 0 + -67 Combine like terms: 0 + -67 = -67 18x + x2 = -67 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -67 + 81 Reorder the terms: 81 + 18x + x2 = -67 + 81 Combine like terms: -67 + 81 = 14 81 + 18x + x2 = 14 Factor a perfect square on the left side: (x + 9)(x + 9) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 9) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 9 = 3.741657387 Simplifying x + 9 = 3.741657387 Reorder the terms: 9 + x = 3.741657387 Solving 9 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 3.741657387 + -9 Combine like terms: 9 + -9 = 0 0 + x = 3.741657387 + -9 x = 3.741657387 + -9 Combine like terms: 3.741657387 + -9 = -5.258342613 x = -5.258342613 Simplifying x = -5.258342613Subproblem 2
x + 9 = -3.741657387 Simplifying x + 9 = -3.741657387 Reorder the terms: 9 + x = -3.741657387 Solving 9 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -3.741657387 + -9 Combine like terms: 9 + -9 = 0 0 + x = -3.741657387 + -9 x = -3.741657387 + -9 Combine like terms: -3.741657387 + -9 = -12.741657387 x = -12.741657387 Simplifying x = -12.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.258342613, -12.741657387}
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