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Simplifying 223x + -0.25x2 + -180 = 0 Reorder the terms: -180 + 223x + -0.25x2 = 0 Solving -180 + 223x + -0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 720 + -892x + x2 = 0 Move the constant term to the right: Add '-720' to each side of the equation. 720 + -892x + -720 + x2 = 0 + -720 Reorder the terms: 720 + -720 + -892x + x2 = 0 + -720 Combine like terms: 720 + -720 = 0 0 + -892x + x2 = 0 + -720 -892x + x2 = 0 + -720 Combine like terms: 0 + -720 = -720 -892x + x2 = -720 The x term is -892x. Take half its coefficient (-446). Square it (198916) and add it to both sides. Add '198916' to each side of the equation. -892x + 198916 + x2 = -720 + 198916 Reorder the terms: 198916 + -892x + x2 = -720 + 198916 Combine like terms: -720 + 198916 = 198196 198916 + -892x + x2 = 198196 Factor a perfect square on the left side: (x + -446)(x + -446) = 198196 Calculate the square root of the right side: 445.192093371 Break this problem into two subproblems by setting (x + -446) equal to 445.192093371 and -445.192093371.Subproblem 1
x + -446 = 445.192093371 Simplifying x + -446 = 445.192093371 Reorder the terms: -446 + x = 445.192093371 Solving -446 + x = 445.192093371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '446' to each side of the equation. -446 + 446 + x = 445.192093371 + 446 Combine like terms: -446 + 446 = 0 0 + x = 445.192093371 + 446 x = 445.192093371 + 446 Combine like terms: 445.192093371 + 446 = 891.192093371 x = 891.192093371 Simplifying x = 891.192093371Subproblem 2
x + -446 = -445.192093371 Simplifying x + -446 = -445.192093371 Reorder the terms: -446 + x = -445.192093371 Solving -446 + x = -445.192093371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '446' to each side of the equation. -446 + 446 + x = -445.192093371 + 446 Combine like terms: -446 + 446 = 0 0 + x = -445.192093371 + 446 x = -445.192093371 + 446 Combine like terms: -445.192093371 + 446 = 0.807906629 x = 0.807906629 Simplifying x = 0.807906629Solution
The solution to the problem is based on the solutions from the subproblems. x = {891.192093371, 0.807906629}
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