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Simplifying (x + 7)(x + 5) = 17 Reorder the terms: (7 + x)(x + 5) = 17 Reorder the terms: (7 + x)(5 + x) = 17 Multiply (7 + x) * (5 + x) (7(5 + x) + x(5 + x)) = 17 ((5 * 7 + x * 7) + x(5 + x)) = 17 ((35 + 7x) + x(5 + x)) = 17 (35 + 7x + (5 * x + x * x)) = 17 (35 + 7x + (5x + x2)) = 17 Combine like terms: 7x + 5x = 12x (35 + 12x + x2) = 17 Solving 35 + 12x + x2 = 17 Solving for variable 'x'. Reorder the terms: 35 + -17 + 12x + x2 = 17 + -17 Combine like terms: 35 + -17 = 18 18 + 12x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 18 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 12x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 12x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 12x + x2 = 0 + -18 12x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 12x + x2 = -18 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -18 + 36 Reorder the terms: 36 + 12x + x2 = -18 + 36 Combine like terms: -18 + 36 = 18 36 + 12x + x2 = 18 Factor a perfect square on the left side: (x + 6)(x + 6) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 6) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 6 = 4.242640687 Simplifying x + 6 = 4.242640687 Reorder the terms: 6 + x = 4.242640687 Solving 6 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.242640687 + -6 x = 4.242640687 + -6 Combine like terms: 4.242640687 + -6 = -1.757359313 x = -1.757359313 Simplifying x = -1.757359313Subproblem 2
x + 6 = -4.242640687 Simplifying x + 6 = -4.242640687 Reorder the terms: 6 + x = -4.242640687 Solving 6 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.242640687 + -6 x = -4.242640687 + -6 Combine like terms: -4.242640687 + -6 = -10.242640687 x = -10.242640687 Simplifying x = -10.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.757359313, -10.242640687}
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