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Simplifying x + x2 = 180 Solving x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + x + x2 = 0 + 180 x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 x + x2 = 180 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 180 + 0.25 Reorder the terms: 0.25 + x + x2 = 180 + 0.25 Combine like terms: 180 + 0.25 = 180.25 0.25 + x + x2 = 180.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + 0.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + 0.5 = 13.425721582 Simplifying x + 0.5 = 13.425721582 Reorder the terms: 0.5 + x = 13.425721582 Solving 0.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.425721582 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.425721582 + -0.5 x = 13.425721582 + -0.5 Combine like terms: 13.425721582 + -0.5 = 12.925721582 x = 12.925721582 Simplifying x = 12.925721582Subproblem 2
x + 0.5 = -13.425721582 Simplifying x + 0.5 = -13.425721582 Reorder the terms: 0.5 + x = -13.425721582 Solving 0.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.425721582 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.425721582 + -0.5 x = -13.425721582 + -0.5 Combine like terms: -13.425721582 + -0.5 = -13.925721582 x = -13.925721582 Simplifying x = -13.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.925721582, -13.925721582}
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