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Simplifying 6x2 + 19x + 4 = 0 Reorder the terms: 4 + 19x + 6x2 = 0 Solving 4 + 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'. 0.6666666667 + 3.166666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 3.166666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 3.166666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 3.166666667x + x2 = 0 + -0.6666666667 3.166666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 3.166666667x + x2 = -0.6666666667 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 = -0.6666666667 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667x + x2 = -0.6666666667 + 2.506944447 Combine like terms: -0.6666666667 + 2.506944447 = 1.8402777803 2.506944447 + 3.166666667x + x2 = 1.8402777803 Factor a perfect square on the left side: (x + 1.583333334)(x + 1.583333334) = 1.8402777803 Calculate the square root of the right side: 1.356568384 Break this problem into two subproblems by setting (x + 1.583333334) equal to 1.356568384 and -1.356568384.Subproblem 1
x + 1.583333334 = 1.356568384 Simplifying x + 1.583333334 = 1.356568384 Reorder the terms: 1.583333334 + x = 1.356568384 Solving 1.583333334 + x = 1.356568384 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 = 1.356568384 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = 1.356568384 + -1.583333334 x = 1.356568384 + -1.583333334 Combine like terms: 1.356568384 + -1.583333334 = -0.22676495 x = -0.22676495 Simplifying x = -0.22676495Subproblem 2
x + 1.583333334 = -1.356568384 Simplifying x + 1.583333334 = -1.356568384 Reorder the terms: 1.583333334 + x = -1.356568384 Solving 1.583333334 + x = -1.356568384 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 = -1.356568384 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = -1.356568384 + -1.583333334 x = -1.356568384 + -1.583333334 Combine like terms: -1.356568384 + -1.583333334 = -2.939901718 x = -2.939901718 Simplifying x = -2.939901718Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.22676495, -2.939901718}
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