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Simplifying (11 + -1x)(15 + -1x) = 50 Multiply (11 + -1x) * (15 + -1x) (11(15 + -1x) + -1x * (15 + -1x)) = 50 ((15 * 11 + -1x * 11) + -1x * (15 + -1x)) = 50 ((165 + -11x) + -1x * (15 + -1x)) = 50 (165 + -11x + (15 * -1x + -1x * -1x)) = 50 (165 + -11x + (-15x + 1x2)) = 50 Combine like terms: -11x + -15x = -26x (165 + -26x + 1x2) = 50 Solving 165 + -26x + 1x2 = 50 Solving for variable 'x'. Reorder the terms: 165 + -50 + -26x + 1x2 = 50 + -50 Combine like terms: 165 + -50 = 115 115 + -26x + 1x2 = 50 + -50 Combine like terms: 50 + -50 = 0 115 + -26x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-115' to each side of the equation. 115 + -26x + -115 + x2 = 0 + -115 Reorder the terms: 115 + -115 + -26x + x2 = 0 + -115 Combine like terms: 115 + -115 = 0 0 + -26x + x2 = 0 + -115 -26x + x2 = 0 + -115 Combine like terms: 0 + -115 = -115 -26x + x2 = -115 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -115 + 169 Reorder the terms: 169 + -26x + x2 = -115 + 169 Combine like terms: -115 + 169 = 54 169 + -26x + x2 = 54 Factor a perfect square on the left side: (x + -13)(x + -13) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -13) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -13 = 7.348469228 Simplifying x + -13 = 7.348469228 Reorder the terms: -13 + x = 7.348469228 Solving -13 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 7.348469228 + 13 Combine like terms: -13 + 13 = 0 0 + x = 7.348469228 + 13 x = 7.348469228 + 13 Combine like terms: 7.348469228 + 13 = 20.348469228 x = 20.348469228 Simplifying x = 20.348469228Subproblem 2
x + -13 = -7.348469228 Simplifying x + -13 = -7.348469228 Reorder the terms: -13 + x = -7.348469228 Solving -13 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -7.348469228 + 13 Combine like terms: -13 + 13 = 0 0 + x = -7.348469228 + 13 x = -7.348469228 + 13 Combine like terms: -7.348469228 + 13 = 5.651530772 x = 5.651530772 Simplifying x = 5.651530772Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.348469228, 5.651530772}
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