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Simplifying 0.683x2 + 6.671x + -799372.381 = 0 Reorder the terms: -799372.381 + 6.671x + 0.683x2 = 0 Solving -799372.381 + 6.671x + 0.683x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.683 the coefficient of the squared term: Divide each side by '0.683'. -1170384.16 + 9.767203514x + x2 = 0 Move the constant term to the right: Add '1170384.16' to each side of the equation. -1170384.16 + 9.767203514x + 1170384.16 + x2 = 0 + 1170384.16 Reorder the terms: -1170384.16 + 1170384.16 + 9.767203514x + x2 = 0 + 1170384.16 Combine like terms: -1170384.16 + 1170384.16 = 0.00 0.00 + 9.767203514x + x2 = 0 + 1170384.16 9.767203514x + x2 = 0 + 1170384.16 Combine like terms: 0 + 1170384.16 = 1170384.16 9.767203514x + x2 = 1170384.16 The x term is 9.767203514x. Take half its coefficient (4.883601757). Square it (23.84956612) and add it to both sides. Add '23.84956612' to each side of the equation. 9.767203514x + 23.84956612 + x2 = 1170384.16 + 23.84956612 Reorder the terms: 23.84956612 + 9.767203514x + x2 = 1170384.16 + 23.84956612 Combine like terms: 1170384.16 + 23.84956612 = 1170408.00956612 23.84956612 + 9.767203514x + x2 = 1170408.00956612 Factor a perfect square on the left side: (x + 4.883601757)(x + 4.883601757) = 1170408.00956612 Calculate the square root of the right side: 1081.853968688 Break this problem into two subproblems by setting (x + 4.883601757) equal to 1081.853968688 and -1081.853968688.Subproblem 1
x + 4.883601757 = 1081.853968688 Simplifying x + 4.883601757 = 1081.853968688 Reorder the terms: 4.883601757 + x = 1081.853968688 Solving 4.883601757 + x = 1081.853968688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.883601757' to each side of the equation. 4.883601757 + -4.883601757 + x = 1081.853968688 + -4.883601757 Combine like terms: 4.883601757 + -4.883601757 = 0.000000000 0.000000000 + x = 1081.853968688 + -4.883601757 x = 1081.853968688 + -4.883601757 Combine like terms: 1081.853968688 + -4.883601757 = 1076.970366931 x = 1076.970366931 Simplifying x = 1076.970366931Subproblem 2
x + 4.883601757 = -1081.853968688 Simplifying x + 4.883601757 = -1081.853968688 Reorder the terms: 4.883601757 + x = -1081.853968688 Solving 4.883601757 + x = -1081.853968688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.883601757' to each side of the equation. 4.883601757 + -4.883601757 + x = -1081.853968688 + -4.883601757 Combine like terms: 4.883601757 + -4.883601757 = 0.000000000 0.000000000 + x = -1081.853968688 + -4.883601757 x = -1081.853968688 + -4.883601757 Combine like terms: -1081.853968688 + -4.883601757 = -1086.737570445 x = -1086.737570445 Simplifying x = -1086.737570445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1076.970366931, -1086.737570445}
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