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Simplifying 0 = -6x2 + 2.2x + 1.21 Reorder the terms: 0 = 1.21 + 2.2x + -6x2 Solving 0 = 1.21 + 2.2x + -6x2 Solving for variable 'x'. Combine like terms: 0 + -1.21 = -1.21 -1.21 + -2.2x + 6x2 = 1.21 + 2.2x + -6x2 + -1.21 + -2.2x + 6x2 Reorder the terms: -1.21 + -2.2x + 6x2 = 1.21 + -1.21 + 2.2x + -2.2x + -6x2 + 6x2 Combine like terms: 1.21 + -1.21 = 0.00 -1.21 + -2.2x + 6x2 = 0.00 + 2.2x + -2.2x + -6x2 + 6x2 -1.21 + -2.2x + 6x2 = 2.2x + -2.2x + -6x2 + 6x2 Combine like terms: 2.2x + -2.2x = 0.0 -1.21 + -2.2x + 6x2 = 0.0 + -6x2 + 6x2 -1.21 + -2.2x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -1.21 + -2.2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.2016666667 + -0.3666666667x + x2 = 0 Move the constant term to the right: Add '0.2016666667' to each side of the equation. -0.2016666667 + -0.3666666667x + 0.2016666667 + x2 = 0 + 0.2016666667 Reorder the terms: -0.2016666667 + 0.2016666667 + -0.3666666667x + x2 = 0 + 0.2016666667 Combine like terms: -0.2016666667 + 0.2016666667 = 0.0000000000 0.0000000000 + -0.3666666667x + x2 = 0 + 0.2016666667 -0.3666666667x + x2 = 0 + 0.2016666667 Combine like terms: 0 + 0.2016666667 = 0.2016666667 -0.3666666667x + x2 = 0.2016666667 The x term is -0.3666666667x. Take half its coefficient (-0.1833333334). Square it (0.03361111114) and add it to both sides. Add '0.03361111114' to each side of the equation. -0.3666666667x + 0.03361111114 + x2 = 0.2016666667 + 0.03361111114 Reorder the terms: 0.03361111114 + -0.3666666667x + x2 = 0.2016666667 + 0.03361111114 Combine like terms: 0.2016666667 + 0.03361111114 = 0.23527777784 0.03361111114 + -0.3666666667x + x2 = 0.23527777784 Factor a perfect square on the left side: (x + -0.1833333334)(x + -0.1833333334) = 0.23527777784 Calculate the square root of the right side: 0.485054407 Break this problem into two subproblems by setting (x + -0.1833333334) equal to 0.485054407 and -0.485054407.Subproblem 1
x + -0.1833333334 = 0.485054407 Simplifying x + -0.1833333334 = 0.485054407 Reorder the terms: -0.1833333334 + x = 0.485054407 Solving -0.1833333334 + x = 0.485054407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1833333334' to each side of the equation. -0.1833333334 + 0.1833333334 + x = 0.485054407 + 0.1833333334 Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000 0.0000000000 + x = 0.485054407 + 0.1833333334 x = 0.485054407 + 0.1833333334 Combine like terms: 0.485054407 + 0.1833333334 = 0.6683877404 x = 0.6683877404 Simplifying x = 0.6683877404Subproblem 2
x + -0.1833333334 = -0.485054407 Simplifying x + -0.1833333334 = -0.485054407 Reorder the terms: -0.1833333334 + x = -0.485054407 Solving -0.1833333334 + x = -0.485054407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1833333334' to each side of the equation. -0.1833333334 + 0.1833333334 + x = -0.485054407 + 0.1833333334 Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000 0.0000000000 + x = -0.485054407 + 0.1833333334 x = -0.485054407 + 0.1833333334 Combine like terms: -0.485054407 + 0.1833333334 = -0.3017210736 x = -0.3017210736 Simplifying x = -0.3017210736Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6683877404, -0.3017210736}
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