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Simplifying (x + 13)(x + 5) = -5 Reorder the terms: (13 + x)(x + 5) = -5 Reorder the terms: (13 + x)(5 + x) = -5 Multiply (13 + x) * (5 + x) (13(5 + x) + x(5 + x)) = -5 ((5 * 13 + x * 13) + x(5 + x)) = -5 ((65 + 13x) + x(5 + x)) = -5 (65 + 13x + (5 * x + x * x)) = -5 (65 + 13x + (5x + x2)) = -5 Combine like terms: 13x + 5x = 18x (65 + 18x + x2) = -5 Solving 65 + 18x + x2 = -5 Solving for variable 'x'. Reorder the terms: 65 + 5 + 18x + x2 = -5 + 5 Combine like terms: 65 + 5 = 70 70 + 18x + x2 = -5 + 5 Combine like terms: -5 + 5 = 0 70 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + 18x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + 18x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + 18x + x2 = 0 + -70 18x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 18x + x2 = -70 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 = -70 + 81 Reorder the terms: 81 + 18x + x2 = -70 + 81 Combine like terms: -70 + 81 = 11 81 + 18x + x2 = 11 Factor a perfect square on the left side: (x + 9)(x + 9) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 9) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 9 = 3.31662479 Simplifying x + 9 = 3.31662479 Reorder the terms: 9 + x = 3.31662479 Solving 9 + x = 3.31662479 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 = 3.31662479 + -9 Combine like terms: 9 + -9 = 0 0 + x = 3.31662479 + -9 x = 3.31662479 + -9 Combine like terms: 3.31662479 + -9 = -5.68337521 x = -5.68337521 Simplifying x = -5.68337521Subproblem 2
x + 9 = -3.31662479 Simplifying x + 9 = -3.31662479 Reorder the terms: 9 + x = -3.31662479 Solving 9 + x = -3.31662479 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 = -3.31662479 + -9 Combine like terms: 9 + -9 = 0 0 + x = -3.31662479 + -9 x = -3.31662479 + -9 Combine like terms: -3.31662479 + -9 = -12.31662479 x = -12.31662479 Simplifying x = -12.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.68337521, -12.31662479}
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