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Simplifying 6x2 + -19x + 11 = 0 Reorder the terms: 11 + -19x + 6x2 = 0 Solving 11 + -19x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -3.166666667x + -1.833333333 + x2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -3.166666667x + x2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + -1.833333333 -3.166666667x + x2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -3.166666667x + x2 = -1.833333333 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 = -1.833333333 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = -1.833333333 + 2.506944447 Combine like terms: -1.833333333 + 2.506944447 = 0.673611114 2.506944447 + -3.166666667x + x2 = 0.673611114 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 0.673611114 Calculate the square root of the right side: 0.820738152 Break this problem into two subproblems by setting (x + -1.583333334) equal to 0.820738152 and -0.820738152.Subproblem 1
x + -1.583333334 = 0.820738152 Simplifying x + -1.583333334 = 0.820738152 Reorder the terms: -1.583333334 + x = 0.820738152 Solving -1.583333334 + x = 0.820738152 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 = 0.820738152 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 0.820738152 + 1.583333334 x = 0.820738152 + 1.583333334 Combine like terms: 0.820738152 + 1.583333334 = 2.404071486 x = 2.404071486 Simplifying x = 2.404071486Subproblem 2
x + -1.583333334 = -0.820738152 Simplifying x + -1.583333334 = -0.820738152 Reorder the terms: -1.583333334 + x = -0.820738152 Solving -1.583333334 + x = -0.820738152 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 = -0.820738152 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -0.820738152 + 1.583333334 x = -0.820738152 + 1.583333334 Combine like terms: -0.820738152 + 1.583333334 = 0.762595182 x = 0.762595182 Simplifying x = 0.762595182Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.404071486, 0.762595182}
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