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Simplifying (x + 11)(x + 5) = -2 Reorder the terms: (11 + x)(x + 5) = -2 Reorder the terms: (11 + x)(5 + x) = -2 Multiply (11 + x) * (5 + x) (11(5 + x) + x(5 + x)) = -2 ((5 * 11 + x * 11) + x(5 + x)) = -2 ((55 + 11x) + x(5 + x)) = -2 (55 + 11x + (5 * x + x * x)) = -2 (55 + 11x + (5x + x2)) = -2 Combine like terms: 11x + 5x = 16x (55 + 16x + x2) = -2 Solving 55 + 16x + x2 = -2 Solving for variable 'x'. Reorder the terms: 55 + 2 + 16x + x2 = -2 + 2 Combine like terms: 55 + 2 = 57 57 + 16x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 57 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-57' to each side of the equation. 57 + 16x + -57 + x2 = 0 + -57 Reorder the terms: 57 + -57 + 16x + x2 = 0 + -57 Combine like terms: 57 + -57 = 0 0 + 16x + x2 = 0 + -57 16x + x2 = 0 + -57 Combine like terms: 0 + -57 = -57 16x + x2 = -57 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -57 + 64 Reorder the terms: 64 + 16x + x2 = -57 + 64 Combine like terms: -57 + 64 = 7 64 + 16x + x2 = 7 Factor a perfect square on the left side: (x + 8)(x + 8) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 8) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 8 = 2.645751311 Simplifying x + 8 = 2.645751311 Reorder the terms: 8 + x = 2.645751311 Solving 8 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 2.645751311 + -8 Combine like terms: 8 + -8 = 0 0 + x = 2.645751311 + -8 x = 2.645751311 + -8 Combine like terms: 2.645751311 + -8 = -5.354248689 x = -5.354248689 Simplifying x = -5.354248689Subproblem 2
x + 8 = -2.645751311 Simplifying x + 8 = -2.645751311 Reorder the terms: 8 + x = -2.645751311 Solving 8 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -2.645751311 + -8 Combine like terms: 8 + -8 = 0 0 + x = -2.645751311 + -8 x = -2.645751311 + -8 Combine like terms: -2.645751311 + -8 = -10.645751311 x = -10.645751311 Simplifying x = -10.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.354248689, -10.645751311}
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