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Simplifying (x + 4)(x + 6) = 160 Reorder the terms: (4 + x)(x + 6) = 160 Reorder the terms: (4 + x)(6 + x) = 160 Multiply (4 + x) * (6 + x) (4(6 + x) + x(6 + x)) = 160 ((6 * 4 + x * 4) + x(6 + x)) = 160 ((24 + 4x) + x(6 + x)) = 160 (24 + 4x + (6 * x + x * x)) = 160 (24 + 4x + (6x + x2)) = 160 Combine like terms: 4x + 6x = 10x (24 + 10x + x2) = 160 Solving 24 + 10x + x2 = 160 Solving for variable 'x'. Reorder the terms: 24 + -160 + 10x + x2 = 160 + -160 Combine like terms: 24 + -160 = -136 -136 + 10x + x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -136 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + 10x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + 10x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + 10x + x2 = 0 + 136 10x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 10x + x2 = 136 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 136 + 25 Reorder the terms: 25 + 10x + x2 = 136 + 25 Combine like terms: 136 + 25 = 161 25 + 10x + x2 = 161 Factor a perfect square on the left side: (x + 5)(x + 5) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + 5) equal to 12.68857754 and -12.68857754.Subproblem 1
x + 5 = 12.68857754 Simplifying x + 5 = 12.68857754 Reorder the terms: 5 + x = 12.68857754 Solving 5 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 12.68857754 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.68857754 + -5 x = 12.68857754 + -5 Combine like terms: 12.68857754 + -5 = 7.68857754 x = 7.68857754 Simplifying x = 7.68857754Subproblem 2
x + 5 = -12.68857754 Simplifying x + 5 = -12.68857754 Reorder the terms: 5 + x = -12.68857754 Solving 5 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -12.68857754 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.68857754 + -5 x = -12.68857754 + -5 Combine like terms: -12.68857754 + -5 = -17.68857754 x = -17.68857754 Simplifying x = -17.68857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.68857754, -17.68857754}
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