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Simplifying -3x2 + 246x + -1100 = 0 Reorder the terms: -1100 + 246x + -3x2 = 0 Solving -1100 + 246x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 366.6666667 + -82x + x2 = 0 Move the constant term to the right: Add '-366.6666667' to each side of the equation. 366.6666667 + -82x + -366.6666667 + x2 = 0 + -366.6666667 Reorder the terms: 366.6666667 + -366.6666667 + -82x + x2 = 0 + -366.6666667 Combine like terms: 366.6666667 + -366.6666667 = 0.0000000 0.0000000 + -82x + x2 = 0 + -366.6666667 -82x + x2 = 0 + -366.6666667 Combine like terms: 0 + -366.6666667 = -366.6666667 -82x + x2 = -366.6666667 The x term is -82x. Take half its coefficient (-41). Square it (1681) and add it to both sides. Add '1681' to each side of the equation. -82x + 1681 + x2 = -366.6666667 + 1681 Reorder the terms: 1681 + -82x + x2 = -366.6666667 + 1681 Combine like terms: -366.6666667 + 1681 = 1314.3333333 1681 + -82x + x2 = 1314.3333333 Factor a perfect square on the left side: (x + -41)(x + -41) = 1314.3333333 Calculate the square root of the right side: 36.253735439 Break this problem into two subproblems by setting (x + -41) equal to 36.253735439 and -36.253735439.Subproblem 1
x + -41 = 36.253735439 Simplifying x + -41 = 36.253735439 Reorder the terms: -41 + x = 36.253735439 Solving -41 + x = 36.253735439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = 36.253735439 + 41 Combine like terms: -41 + 41 = 0 0 + x = 36.253735439 + 41 x = 36.253735439 + 41 Combine like terms: 36.253735439 + 41 = 77.253735439 x = 77.253735439 Simplifying x = 77.253735439Subproblem 2
x + -41 = -36.253735439 Simplifying x + -41 = -36.253735439 Reorder the terms: -41 + x = -36.253735439 Solving -41 + x = -36.253735439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = -36.253735439 + 41 Combine like terms: -41 + 41 = 0 0 + x = -36.253735439 + 41 x = -36.253735439 + 41 Combine like terms: -36.253735439 + 41 = 4.746264561 x = 4.746264561 Simplifying x = 4.746264561Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.253735439, 4.746264561}
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