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Simplifying 6x2 = -19x + -1 Reorder the terms: 6x2 = -1 + -19x Solving 6x2 = -1 + -19x Solving for variable 'x'. Reorder the terms: 1 + 19x + 6x2 = -1 + -19x + 1 + 19x Reorder the terms: 1 + 19x + 6x2 = -1 + 1 + -19x + 19x Combine like terms: -1 + 1 = 0 1 + 19x + 6x2 = 0 + -19x + 19x 1 + 19x + 6x2 = -19x + 19x Combine like terms: -19x + 19x = 0 1 + 19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 3.166666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 3.166666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 3.166666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 3.166666667x + x2 = 0 + -0.1666666667 3.166666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 3.166666667x + x2 = -0.1666666667 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 = -0.1666666667 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667x + x2 = -0.1666666667 + 2.506944447 Combine like terms: -0.1666666667 + 2.506944447 = 2.3402777803 2.506944447 + 3.166666667x + x2 = 2.3402777803 Factor a perfect square on the left side: (x + 1.583333334)(x + 1.583333334) = 2.3402777803 Calculate the square root of the right side: 1.529796647 Break this problem into two subproblems by setting (x + 1.583333334) equal to 1.529796647 and -1.529796647.Subproblem 1
x + 1.583333334 = 1.529796647 Simplifying x + 1.583333334 = 1.529796647 Reorder the terms: 1.583333334 + x = 1.529796647 Solving 1.583333334 + x = 1.529796647 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 = 1.529796647 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = 1.529796647 + -1.583333334 x = 1.529796647 + -1.583333334 Combine like terms: 1.529796647 + -1.583333334 = -0.053536687 x = -0.053536687 Simplifying x = -0.053536687Subproblem 2
x + 1.583333334 = -1.529796647 Simplifying x + 1.583333334 = -1.529796647 Reorder the terms: 1.583333334 + x = -1.529796647 Solving 1.583333334 + x = -1.529796647 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 = -1.529796647 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = -1.529796647 + -1.583333334 x = -1.529796647 + -1.583333334 Combine like terms: -1.529796647 + -1.583333334 = -3.113129981 x = -3.113129981 Simplifying x = -3.113129981Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.053536687, -3.113129981}
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