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Simplifying 6x2 + -19x = 73 Reorder the terms: -19x + 6x2 = 73 Solving -19x + 6x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + -19x + 6x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -12.16666667 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '12.16666667' to each side of the equation. -12.16666667 + -3.166666667x + 12.16666667 + x2 = 0 + 12.16666667 Reorder the terms: -12.16666667 + 12.16666667 + -3.166666667x + x2 = 0 + 12.16666667 Combine like terms: -12.16666667 + 12.16666667 = 0.00000000 0.00000000 + -3.166666667x + x2 = 0 + 12.16666667 -3.166666667x + x2 = 0 + 12.16666667 Combine like terms: 0 + 12.16666667 = 12.16666667 -3.166666667x + x2 = 12.16666667 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = 12.16666667 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 12.16666667 + 2.506944447 Combine like terms: 12.16666667 + 2.506944447 = 14.673611117 2.506944447 + -3.166666667x + x2 = 14.673611117 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 14.673611117 Calculate the square root of the right side: 3.830614979 Break this problem into two subproblems by setting (x + -1.583333334) equal to 3.830614979 and -3.830614979.Subproblem 1
x + -1.583333334 = 3.830614979 Simplifying x + -1.583333334 = 3.830614979 Reorder the terms: -1.583333334 + x = 3.830614979 Solving -1.583333334 + x = 3.830614979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 3.830614979 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 3.830614979 + 1.583333334 x = 3.830614979 + 1.583333334 Combine like terms: 3.830614979 + 1.583333334 = 5.413948313 x = 5.413948313 Simplifying x = 5.413948313Subproblem 2
x + -1.583333334 = -3.830614979 Simplifying x + -1.583333334 = -3.830614979 Reorder the terms: -1.583333334 + x = -3.830614979 Solving -1.583333334 + x = -3.830614979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -3.830614979 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -3.830614979 + 1.583333334 x = -3.830614979 + 1.583333334 Combine like terms: -3.830614979 + 1.583333334 = -2.247281645 x = -2.247281645 Simplifying x = -2.247281645Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.413948313, -2.247281645}
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