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Simplifying (x + 5)(x + 6) = 130 Reorder the terms: (5 + x)(x + 6) = 130 Reorder the terms: (5 + x)(6 + x) = 130 Multiply (5 + x) * (6 + x) (5(6 + x) + x(6 + x)) = 130 ((6 * 5 + x * 5) + x(6 + x)) = 130 ((30 + 5x) + x(6 + x)) = 130 (30 + 5x + (6 * x + x * x)) = 130 (30 + 5x + (6x + x2)) = 130 Combine like terms: 5x + 6x = 11x (30 + 11x + x2) = 130 Solving 30 + 11x + x2 = 130 Solving for variable 'x'. Reorder the terms: 30 + -130 + 11x + x2 = 130 + -130 Combine like terms: 30 + -130 = -100 -100 + 11x + x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -100 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 11x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 11x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 11x + x2 = 0 + 100 11x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 11x + x2 = 100 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 = 100 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 100 + 30.25 Combine like terms: 100 + 30.25 = 130.25 30.25 + 11x + x2 = 130.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + 5.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + 5.5 = 11.412712211 Simplifying x + 5.5 = 11.412712211 Reorder the terms: 5.5 + x = 11.412712211 Solving 5.5 + x = 11.412712211 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 = 11.412712211 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 11.412712211 + -5.5 x = 11.412712211 + -5.5 Combine like terms: 11.412712211 + -5.5 = 5.912712211 x = 5.912712211 Simplifying x = 5.912712211Subproblem 2
x + 5.5 = -11.412712211 Simplifying x + 5.5 = -11.412712211 Reorder the terms: 5.5 + x = -11.412712211 Solving 5.5 + x = -11.412712211 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 = -11.412712211 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -11.412712211 + -5.5 x = -11.412712211 + -5.5 Combine like terms: -11.412712211 + -5.5 = -16.912712211 x = -16.912712211 Simplifying x = -16.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.912712211, -16.912712211}
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