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Simplifying (x + 12)(x + 2) = 168 Reorder the terms: (12 + x)(x + 2) = 168 Reorder the terms: (12 + x)(2 + x) = 168 Multiply (12 + x) * (2 + x) (12(2 + x) + x(2 + x)) = 168 ((2 * 12 + x * 12) + x(2 + x)) = 168 ((24 + 12x) + x(2 + x)) = 168 (24 + 12x + (2 * x + x * x)) = 168 (24 + 12x + (2x + x2)) = 168 Combine like terms: 12x + 2x = 14x (24 + 14x + x2) = 168 Solving 24 + 14x + x2 = 168 Solving for variable 'x'. Reorder the terms: 24 + -168 + 14x + x2 = 168 + -168 Combine like terms: 24 + -168 = -144 -144 + 14x + x2 = 168 + -168 Combine like terms: 168 + -168 = 0 -144 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 14x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 14x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 14x + x2 = 0 + 144 14x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 14x + x2 = 144 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 144 + 49 Reorder the terms: 49 + 14x + x2 = 144 + 49 Combine like terms: 144 + 49 = 193 49 + 14x + x2 = 193 Factor a perfect square on the left side: (x + 7)(x + 7) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + 7) equal to 13.892443989 and -13.892443989.Subproblem 1
x + 7 = 13.892443989 Simplifying x + 7 = 13.892443989 Reorder the terms: 7 + x = 13.892443989 Solving 7 + x = 13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 13.892443989 + -7 Combine like terms: 7 + -7 = 0 0 + x = 13.892443989 + -7 x = 13.892443989 + -7 Combine like terms: 13.892443989 + -7 = 6.892443989 x = 6.892443989 Simplifying x = 6.892443989Subproblem 2
x + 7 = -13.892443989 Simplifying x + 7 = -13.892443989 Reorder the terms: 7 + x = -13.892443989 Solving 7 + x = -13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -13.892443989 + -7 Combine like terms: 7 + -7 = 0 0 + x = -13.892443989 + -7 x = -13.892443989 + -7 Combine like terms: -13.892443989 + -7 = -20.892443989 x = -20.892443989 Simplifying x = -20.892443989Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.892443989, -20.892443989}
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