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Simplifying (x + 7)(x + 11) = 1 Reorder the terms: (7 + x)(x + 11) = 1 Reorder the terms: (7 + x)(11 + x) = 1 Multiply (7 + x) * (11 + x) (7(11 + x) + x(11 + x)) = 1 ((11 * 7 + x * 7) + x(11 + x)) = 1 ((77 + 7x) + x(11 + x)) = 1 (77 + 7x + (11 * x + x * x)) = 1 (77 + 7x + (11x + x2)) = 1 Combine like terms: 7x + 11x = 18x (77 + 18x + x2) = 1 Solving 77 + 18x + x2 = 1 Solving for variable 'x'. Reorder the terms: 77 + -1 + 18x + x2 = 1 + -1 Combine like terms: 77 + -1 = 76 76 + 18x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 76 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-76' to each side of the equation. 76 + 18x + -76 + x2 = 0 + -76 Reorder the terms: 76 + -76 + 18x + x2 = 0 + -76 Combine like terms: 76 + -76 = 0 0 + 18x + x2 = 0 + -76 18x + x2 = 0 + -76 Combine like terms: 0 + -76 = -76 18x + x2 = -76 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -76 + 81 Reorder the terms: 81 + 18x + x2 = -76 + 81 Combine like terms: -76 + 81 = 5 81 + 18x + x2 = 5 Factor a perfect square on the left side: (x + 9)(x + 9) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 9) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 9 = 2.236067978 Simplifying x + 9 = 2.236067978 Reorder the terms: 9 + x = 2.236067978 Solving 9 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 2.236067978 + -9 Combine like terms: 9 + -9 = 0 0 + x = 2.236067978 + -9 x = 2.236067978 + -9 Combine like terms: 2.236067978 + -9 = -6.763932022 x = -6.763932022 Simplifying x = -6.763932022Subproblem 2
x + 9 = -2.236067978 Simplifying x + 9 = -2.236067978 Reorder the terms: 9 + x = -2.236067978 Solving 9 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -2.236067978 + -9 Combine like terms: 9 + -9 = 0 0 + x = -2.236067978 + -9 x = -2.236067978 + -9 Combine like terms: -2.236067978 + -9 = -11.236067978 x = -11.236067978 Simplifying x = -11.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.763932022, -11.236067978}
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