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Simplifying (x + 17)(x + 9) = -5 Reorder the terms: (17 + x)(x + 9) = -5 Reorder the terms: (17 + x)(9 + x) = -5 Multiply (17 + x) * (9 + x) (17(9 + x) + x(9 + x)) = -5 ((9 * 17 + x * 17) + x(9 + x)) = -5 ((153 + 17x) + x(9 + x)) = -5 (153 + 17x + (9 * x + x * x)) = -5 (153 + 17x + (9x + x2)) = -5 Combine like terms: 17x + 9x = 26x (153 + 26x + x2) = -5 Solving 153 + 26x + x2 = -5 Solving for variable 'x'. Reorder the terms: 153 + 5 + 26x + x2 = -5 + 5 Combine like terms: 153 + 5 = 158 158 + 26x + x2 = -5 + 5 Combine like terms: -5 + 5 = 0 158 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-158' to each side of the equation. 158 + 26x + -158 + x2 = 0 + -158 Reorder the terms: 158 + -158 + 26x + x2 = 0 + -158 Combine like terms: 158 + -158 = 0 0 + 26x + x2 = 0 + -158 26x + x2 = 0 + -158 Combine like terms: 0 + -158 = -158 26x + x2 = -158 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -158 + 169 Reorder the terms: 169 + 26x + x2 = -158 + 169 Combine like terms: -158 + 169 = 11 169 + 26x + x2 = 11 Factor a perfect square on the left side: (x + 13)(x + 13) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 13) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 13 = 3.31662479 Simplifying x + 13 = 3.31662479 Reorder the terms: 13 + x = 3.31662479 Solving 13 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 3.31662479 + -13 Combine like terms: 13 + -13 = 0 0 + x = 3.31662479 + -13 x = 3.31662479 + -13 Combine like terms: 3.31662479 + -13 = -9.68337521 x = -9.68337521 Simplifying x = -9.68337521Subproblem 2
x + 13 = -3.31662479 Simplifying x + 13 = -3.31662479 Reorder the terms: 13 + x = -3.31662479 Solving 13 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -3.31662479 + -13 Combine like terms: 13 + -13 = 0 0 + x = -3.31662479 + -13 x = -3.31662479 + -13 Combine like terms: -3.31662479 + -13 = -16.31662479 x = -16.31662479 Simplifying x = -16.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.68337521, -16.31662479}
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