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Simplifying (x + 5)(x + 6) = 104 Reorder the terms: (5 + x)(x + 6) = 104 Reorder the terms: (5 + x)(6 + x) = 104 Multiply (5 + x) * (6 + x) (5(6 + x) + x(6 + x)) = 104 ((6 * 5 + x * 5) + x(6 + x)) = 104 ((30 + 5x) + x(6 + x)) = 104 (30 + 5x + (6 * x + x * x)) = 104 (30 + 5x + (6x + x2)) = 104 Combine like terms: 5x + 6x = 11x (30 + 11x + x2) = 104 Solving 30 + 11x + x2 = 104 Solving for variable 'x'. Reorder the terms: 30 + -104 + 11x + x2 = 104 + -104 Combine like terms: 30 + -104 = -74 -74 + 11x + x2 = 104 + -104 Combine like terms: 104 + -104 = 0 -74 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 11x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + 11x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 11x + x2 = 0 + 74 11x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 11x + x2 = 74 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 74 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 74 + 30.25 Combine like terms: 74 + 30.25 = 104.25 30.25 + 11x + x2 = 104.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + 5.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + 5.5 = 10.210288928 Simplifying x + 5.5 = 10.210288928 Reorder the terms: 5.5 + x = 10.210288928 Solving 5.5 + x = 10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 10.210288928 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 10.210288928 + -5.5 x = 10.210288928 + -5.5 Combine like terms: 10.210288928 + -5.5 = 4.710288928 x = 4.710288928 Simplifying x = 4.710288928Subproblem 2
x + 5.5 = -10.210288928 Simplifying x + 5.5 = -10.210288928 Reorder the terms: 5.5 + x = -10.210288928 Solving 5.5 + x = -10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -10.210288928 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -10.210288928 + -5.5 x = -10.210288928 + -5.5 Combine like terms: -10.210288928 + -5.5 = -15.710288928 x = -15.710288928 Simplifying x = -15.710288928Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.710288928, -15.710288928}
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