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Simplifying x2 + 27x + -46 = 0 Reorder the terms: -46 + 27x + x2 = 0 Solving -46 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 27x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 27x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 27x + x2 = 0 + 46 27x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 27x + x2 = 46 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 46 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 46 + 182.25 Combine like terms: 46 + 182.25 = 228.25 182.25 + 27x + x2 = 228.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 228.25 Calculate the square root of the right side: 15.10794493 Break this problem into two subproblems by setting (x + 13.5) equal to 15.10794493 and -15.10794493.Subproblem 1
x + 13.5 = 15.10794493 Simplifying x + 13.5 = 15.10794493 Reorder the terms: 13.5 + x = 15.10794493 Solving 13.5 + x = 15.10794493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 15.10794493 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 15.10794493 + -13.5 x = 15.10794493 + -13.5 Combine like terms: 15.10794493 + -13.5 = 1.60794493 x = 1.60794493 Simplifying x = 1.60794493Subproblem 2
x + 13.5 = -15.10794493 Simplifying x + 13.5 = -15.10794493 Reorder the terms: 13.5 + x = -15.10794493 Solving 13.5 + x = -15.10794493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -15.10794493 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -15.10794493 + -13.5 x = -15.10794493 + -13.5 Combine like terms: -15.10794493 + -13.5 = -28.60794493 x = -28.60794493 Simplifying x = -28.60794493Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.60794493, -28.60794493}
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