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Simplifying 6x2 + -19x + -5 = 0 Reorder the terms: -5 + -19x + 6x2 = 0 Solving -5 + -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'. -0.8333333333 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -3.166666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -3.166666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -3.166666667x + x2 = 0 + 0.8333333333 -3.166666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -3.166666667x + x2 = 0.8333333333 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 = 0.8333333333 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 0.8333333333 + 2.506944447 Combine like terms: 0.8333333333 + 2.506944447 = 3.3402777803 2.506944447 + -3.166666667x + x2 = 3.3402777803 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 3.3402777803 Calculate the square root of the right side: 1.827642684 Break this problem into two subproblems by setting (x + -1.583333334) equal to 1.827642684 and -1.827642684.Subproblem 1
x + -1.583333334 = 1.827642684 Simplifying x + -1.583333334 = 1.827642684 Reorder the terms: -1.583333334 + x = 1.827642684 Solving -1.583333334 + x = 1.827642684 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 = 1.827642684 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 1.827642684 + 1.583333334 x = 1.827642684 + 1.583333334 Combine like terms: 1.827642684 + 1.583333334 = 3.410976018 x = 3.410976018 Simplifying x = 3.410976018Subproblem 2
x + -1.583333334 = -1.827642684 Simplifying x + -1.583333334 = -1.827642684 Reorder the terms: -1.583333334 + x = -1.827642684 Solving -1.583333334 + x = -1.827642684 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 = -1.827642684 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -1.827642684 + 1.583333334 x = -1.827642684 + 1.583333334 Combine like terms: -1.827642684 + 1.583333334 = -0.24430935 x = -0.24430935 Simplifying x = -0.24430935Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.410976018, -0.24430935}
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