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Simplifying (x + 8)(x + -2) = 169 Reorder the terms: (8 + x)(x + -2) = 169 Reorder the terms: (8 + x)(-2 + x) = 169 Multiply (8 + x) * (-2 + x) (8(-2 + x) + x(-2 + x)) = 169 ((-2 * 8 + x * 8) + x(-2 + x)) = 169 ((-16 + 8x) + x(-2 + x)) = 169 (-16 + 8x + (-2 * x + x * x)) = 169 (-16 + 8x + (-2x + x2)) = 169 Combine like terms: 8x + -2x = 6x (-16 + 6x + x2) = 169 Solving -16 + 6x + x2 = 169 Solving for variable 'x'. Reorder the terms: -16 + -169 + 6x + x2 = 169 + -169 Combine like terms: -16 + -169 = -185 -185 + 6x + x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -185 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '185' to each side of the equation. -185 + 6x + 185 + x2 = 0 + 185 Reorder the terms: -185 + 185 + 6x + x2 = 0 + 185 Combine like terms: -185 + 185 = 0 0 + 6x + x2 = 0 + 185 6x + x2 = 0 + 185 Combine like terms: 0 + 185 = 185 6x + x2 = 185 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 185 + 9 Reorder the terms: 9 + 6x + x2 = 185 + 9 Combine like terms: 185 + 9 = 194 9 + 6x + x2 = 194 Factor a perfect square on the left side: (x + 3)(x + 3) = 194 Calculate the square root of the right side: 13.928388277 Break this problem into two subproblems by setting (x + 3) equal to 13.928388277 and -13.928388277.Subproblem 1
x + 3 = 13.928388277 Simplifying x + 3 = 13.928388277 Reorder the terms: 3 + x = 13.928388277 Solving 3 + x = 13.928388277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 13.928388277 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.928388277 + -3 x = 13.928388277 + -3 Combine like terms: 13.928388277 + -3 = 10.928388277 x = 10.928388277 Simplifying x = 10.928388277Subproblem 2
x + 3 = -13.928388277 Simplifying x + 3 = -13.928388277 Reorder the terms: 3 + x = -13.928388277 Solving 3 + x = -13.928388277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -13.928388277 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.928388277 + -3 x = -13.928388277 + -3 Combine like terms: -13.928388277 + -3 = -16.928388277 x = -16.928388277 Simplifying x = -16.928388277Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.928388277, -16.928388277}
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