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Simplifying (x + 1)(x + 2) = 180 Reorder the terms: (1 + x)(x + 2) = 180 Reorder the terms: (1 + x)(2 + x) = 180 Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x)) = 180 ((2 * 1 + x * 1) + x(2 + x)) = 180 ((2 + 1x) + x(2 + x)) = 180 (2 + 1x + (2 * x + x * x)) = 180 (2 + 1x + (2x + x2)) = 180 Combine like terms: 1x + 2x = 3x (2 + 3x + x2) = 180 Solving 2 + 3x + x2 = 180 Solving for variable 'x'. Reorder the terms: 2 + -180 + 3x + x2 = 180 + -180 Combine like terms: 2 + -180 = -178 -178 + 3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -178 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '178' to each side of the equation. -178 + 3x + 178 + x2 = 0 + 178 Reorder the terms: -178 + 178 + 3x + x2 = 0 + 178 Combine like terms: -178 + 178 = 0 0 + 3x + x2 = 0 + 178 3x + x2 = 0 + 178 Combine like terms: 0 + 178 = 178 3x + x2 = 178 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 178 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 178 + 2.25 Combine like terms: 178 + 2.25 = 180.25 2.25 + 3x + x2 = 180.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + 1.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + 1.5 = 13.425721582 Simplifying x + 1.5 = 13.425721582 Reorder the terms: 1.5 + x = 13.425721582 Solving 1.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 13.425721582 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.425721582 + -1.5 x = 13.425721582 + -1.5 Combine like terms: 13.425721582 + -1.5 = 11.925721582 x = 11.925721582 Simplifying x = 11.925721582Subproblem 2
x + 1.5 = -13.425721582 Simplifying x + 1.5 = -13.425721582 Reorder the terms: 1.5 + x = -13.425721582 Solving 1.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -13.425721582 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.425721582 + -1.5 x = -13.425721582 + -1.5 Combine like terms: -13.425721582 + -1.5 = -14.925721582 x = -14.925721582 Simplifying x = -14.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.925721582, -14.925721582}
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