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Simplifying 6x2 + -19x + -7 = 6 Reorder the terms: -7 + -19x + 6x2 = 6 Solving -7 + -19x + 6x2 = 6 Solving for variable 'x'. Reorder the terms: -7 + -6 + -19x + 6x2 = 6 + -6 Combine like terms: -7 + -6 = -13 -13 + -19x + 6x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -13 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + -3.166666667x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + -3.166666667x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + 2.166666667 -3.166666667x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 -3.166666667x + x2 = 2.166666667 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 = 2.166666667 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 2.166666667 + 2.506944447 Combine like terms: 2.166666667 + 2.506944447 = 4.673611114 2.506944447 + -3.166666667x + x2 = 4.673611114 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 4.673611114 Calculate the square root of the right side: 2.161853629 Break this problem into two subproblems by setting (x + -1.583333334) equal to 2.161853629 and -2.161853629.Subproblem 1
x + -1.583333334 = 2.161853629 Simplifying x + -1.583333334 = 2.161853629 Reorder the terms: -1.583333334 + x = 2.161853629 Solving -1.583333334 + x = 2.161853629 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 = 2.161853629 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 2.161853629 + 1.583333334 x = 2.161853629 + 1.583333334 Combine like terms: 2.161853629 + 1.583333334 = 3.745186963 x = 3.745186963 Simplifying x = 3.745186963Subproblem 2
x + -1.583333334 = -2.161853629 Simplifying x + -1.583333334 = -2.161853629 Reorder the terms: -1.583333334 + x = -2.161853629 Solving -1.583333334 + x = -2.161853629 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 = -2.161853629 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -2.161853629 + 1.583333334 x = -2.161853629 + 1.583333334 Combine like terms: -2.161853629 + 1.583333334 = -0.578520295 x = -0.578520295 Simplifying x = -0.578520295Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.745186963, -0.578520295}
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