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Simplifying (x + 1)(x + 3) = 132 Reorder the terms: (1 + x)(x + 3) = 132 Reorder the terms: (1 + x)(3 + x) = 132 Multiply (1 + x) * (3 + x) (1(3 + x) + x(3 + x)) = 132 ((3 * 1 + x * 1) + x(3 + x)) = 132 ((3 + 1x) + x(3 + x)) = 132 (3 + 1x + (3 * x + x * x)) = 132 (3 + 1x + (3x + x2)) = 132 Combine like terms: 1x + 3x = 4x (3 + 4x + x2) = 132 Solving 3 + 4x + x2 = 132 Solving for variable 'x'. Reorder the terms: 3 + -132 + 4x + x2 = 132 + -132 Combine like terms: 3 + -132 = -129 -129 + 4x + x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -129 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '129' to each side of the equation. -129 + 4x + 129 + x2 = 0 + 129 Reorder the terms: -129 + 129 + 4x + x2 = 0 + 129 Combine like terms: -129 + 129 = 0 0 + 4x + x2 = 0 + 129 4x + x2 = 0 + 129 Combine like terms: 0 + 129 = 129 4x + x2 = 129 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 129 + 4 Reorder the terms: 4 + 4x + x2 = 129 + 4 Combine like terms: 129 + 4 = 133 4 + 4x + x2 = 133 Factor a perfect square on the left side: (x + 2)(x + 2) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + 2) equal to 11.532562595 and -11.532562595.Subproblem 1
x + 2 = 11.532562595 Simplifying x + 2 = 11.532562595 Reorder the terms: 2 + x = 11.532562595 Solving 2 + x = 11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 11.532562595 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.532562595 + -2 x = 11.532562595 + -2 Combine like terms: 11.532562595 + -2 = 9.532562595 x = 9.532562595 Simplifying x = 9.532562595Subproblem 2
x + 2 = -11.532562595 Simplifying x + 2 = -11.532562595 Reorder the terms: 2 + x = -11.532562595 Solving 2 + x = -11.532562595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -11.532562595 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.532562595 + -2 x = -11.532562595 + -2 Combine like terms: -11.532562595 + -2 = -13.532562595 x = -13.532562595 Simplifying x = -13.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.532562595, -13.532562595}
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