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Simplifying (9 + x)(13 + x) = 135 Multiply (9 + x) * (13 + x) (9(13 + x) + x(13 + x)) = 135 ((13 * 9 + x * 9) + x(13 + x)) = 135 ((117 + 9x) + x(13 + x)) = 135 (117 + 9x + (13 * x + x * x)) = 135 (117 + 9x + (13x + x2)) = 135 Combine like terms: 9x + 13x = 22x (117 + 22x + x2) = 135 Solving 117 + 22x + x2 = 135 Solving for variable 'x'. Reorder the terms: 117 + -135 + 22x + x2 = 135 + -135 Combine like terms: 117 + -135 = -18 -18 + 22x + x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -18 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 22x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 22x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 22x + x2 = 0 + 18 22x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 22x + x2 = 18 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 18 + 121 Reorder the terms: 121 + 22x + x2 = 18 + 121 Combine like terms: 18 + 121 = 139 121 + 22x + x2 = 139 Factor a perfect square on the left side: (x + 11)(x + 11) = 139 Calculate the square root of the right side: 11.789826123 Break this problem into two subproblems by setting (x + 11) equal to 11.789826123 and -11.789826123.Subproblem 1
x + 11 = 11.789826123 Simplifying x + 11 = 11.789826123 Reorder the terms: 11 + x = 11.789826123 Solving 11 + x = 11.789826123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 11.789826123 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.789826123 + -11 x = 11.789826123 + -11 Combine like terms: 11.789826123 + -11 = 0.789826123 x = 0.789826123 Simplifying x = 0.789826123Subproblem 2
x + 11 = -11.789826123 Simplifying x + 11 = -11.789826123 Reorder the terms: 11 + x = -11.789826123 Solving 11 + x = -11.789826123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -11.789826123 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.789826123 + -11 x = -11.789826123 + -11 Combine like terms: -11.789826123 + -11 = -22.789826123 x = -22.789826123 Simplifying x = -22.789826123Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.789826123, -22.789826123}
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