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Simplifying 9x2 + -123x + -734 = 0 Reorder the terms: -734 + -123x + 9x2 = 0 Solving -734 + -123x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -81.55555556 + -13.66666667x + x2 = 0 Move the constant term to the right: Add '81.55555556' to each side of the equation. -81.55555556 + -13.66666667x + 81.55555556 + x2 = 0 + 81.55555556 Reorder the terms: -81.55555556 + 81.55555556 + -13.66666667x + x2 = 0 + 81.55555556 Combine like terms: -81.55555556 + 81.55555556 = 0.00000000 0.00000000 + -13.66666667x + x2 = 0 + 81.55555556 -13.66666667x + x2 = 0 + 81.55555556 Combine like terms: 0 + 81.55555556 = 81.55555556 -13.66666667x + x2 = 81.55555556 The x term is -13.66666667x. Take half its coefficient (-6.833333335). Square it (46.69444447) and add it to both sides. Add '46.69444447' to each side of the equation. -13.66666667x + 46.69444447 + x2 = 81.55555556 + 46.69444447 Reorder the terms: 46.69444447 + -13.66666667x + x2 = 81.55555556 + 46.69444447 Combine like terms: 81.55555556 + 46.69444447 = 128.25000003 46.69444447 + -13.66666667x + x2 = 128.25000003 Factor a perfect square on the left side: (x + -6.833333335)(x + -6.833333335) = 128.25000003 Calculate the square root of the right side: 11.324751654 Break this problem into two subproblems by setting (x + -6.833333335) equal to 11.324751654 and -11.324751654.Subproblem 1
x + -6.833333335 = 11.324751654 Simplifying x + -6.833333335 = 11.324751654 Reorder the terms: -6.833333335 + x = 11.324751654 Solving -6.833333335 + x = 11.324751654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = 11.324751654 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 11.324751654 + 6.833333335 x = 11.324751654 + 6.833333335 Combine like terms: 11.324751654 + 6.833333335 = 18.158084989 x = 18.158084989 Simplifying x = 18.158084989Subproblem 2
x + -6.833333335 = -11.324751654 Simplifying x + -6.833333335 = -11.324751654 Reorder the terms: -6.833333335 + x = -11.324751654 Solving -6.833333335 + x = -11.324751654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = -11.324751654 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -11.324751654 + 6.833333335 x = -11.324751654 + 6.833333335 Combine like terms: -11.324751654 + 6.833333335 = -4.491418319 x = -4.491418319 Simplifying x = -4.491418319Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.158084989, -4.491418319}
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