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Simplifying -0.25x2 + 223x + -45760 = 0 Reorder the terms: -45760 + 223x + -0.25x2 = 0 Solving -45760 + 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'. 183040 + -892x + x2 = 0 Move the constant term to the right: Add '-183040' to each side of the equation. 183040 + -892x + -183040 + x2 = 0 + -183040 Reorder the terms: 183040 + -183040 + -892x + x2 = 0 + -183040 Combine like terms: 183040 + -183040 = 0 0 + -892x + x2 = 0 + -183040 -892x + x2 = 0 + -183040 Combine like terms: 0 + -183040 = -183040 -892x + x2 = -183040 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 = -183040 + 198916 Reorder the terms: 198916 + -892x + x2 = -183040 + 198916 Combine like terms: -183040 + 198916 = 15876 198916 + -892x + x2 = 15876 Factor a perfect square on the left side: (x + -446)(x + -446) = 15876 Calculate the square root of the right side: 126 Break this problem into two subproblems by setting (x + -446) equal to 126 and -126.Subproblem 1
x + -446 = 126 Simplifying x + -446 = 126 Reorder the terms: -446 + x = 126 Solving -446 + x = 126 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 = 126 + 446 Combine like terms: -446 + 446 = 0 0 + x = 126 + 446 x = 126 + 446 Combine like terms: 126 + 446 = 572 x = 572 Simplifying x = 572Subproblem 2
x + -446 = -126 Simplifying x + -446 = -126 Reorder the terms: -446 + x = -126 Solving -446 + x = -126 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 = -126 + 446 Combine like terms: -446 + 446 = 0 0 + x = -126 + 446 x = -126 + 446 Combine like terms: -126 + 446 = 320 x = 320 Simplifying x = 320Solution
The solution to the problem is based on the solutions from the subproblems. x = {572, 320}
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