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Simplifying x2 + 12x + 11 = 113 Reorder the terms: 11 + 12x + x2 = 113 Solving 11 + 12x + x2 = 113 Solving for variable 'x'. Reorder the terms: 11 + -113 + 12x + x2 = 113 + -113 Combine like terms: 11 + -113 = -102 -102 + 12x + x2 = 113 + -113 Combine like terms: 113 + -113 = 0 -102 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + 12x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 12x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 12x + x2 = 0 + 102 12x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 12x + x2 = 102 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 102 + 36 Reorder the terms: 36 + 12x + x2 = 102 + 36 Combine like terms: 102 + 36 = 138 36 + 12x + x2 = 138 Factor a perfect square on the left side: (x + 6)(x + 6) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (x + 6) equal to 11.747340124 and -11.747340124.Subproblem 1
x + 6 = 11.747340124 Simplifying x + 6 = 11.747340124 Reorder the terms: 6 + x = 11.747340124 Solving 6 + x = 11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 11.747340124 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.747340124 + -6 x = 11.747340124 + -6 Combine like terms: 11.747340124 + -6 = 5.747340124 x = 5.747340124 Simplifying x = 5.747340124Subproblem 2
x + 6 = -11.747340124 Simplifying x + 6 = -11.747340124 Reorder the terms: 6 + x = -11.747340124 Solving 6 + x = -11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -11.747340124 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.747340124 + -6 x = -11.747340124 + -6 Combine like terms: -11.747340124 + -6 = -17.747340124 x = -17.747340124 Simplifying x = -17.747340124Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.747340124, -17.747340124}
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