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Simplifying 6x2 + 19x + 12 = 0 Reorder the terms: 12 + 19x + 6x2 = 0 Solving 12 + 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'. 2 + 3.166666667x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.166666667x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.166666667x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.166666667x + x2 = 0 + -2 3.166666667x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.166666667x + x2 = -2 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 = -2 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667x + x2 = -2 + 2.506944447 Combine like terms: -2 + 2.506944447 = 0.506944447 2.506944447 + 3.166666667x + x2 = 0.506944447 Factor a perfect square on the left side: (x + 1.583333334)(x + 1.583333334) = 0.506944447 Calculate the square root of the right side: 0.712000314 Break this problem into two subproblems by setting (x + 1.583333334) equal to 0.712000314 and -0.712000314.Subproblem 1
x + 1.583333334 = 0.712000314 Simplifying x + 1.583333334 = 0.712000314 Reorder the terms: 1.583333334 + x = 0.712000314 Solving 1.583333334 + x = 0.712000314 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 = 0.712000314 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = 0.712000314 + -1.583333334 x = 0.712000314 + -1.583333334 Combine like terms: 0.712000314 + -1.583333334 = -0.87133302 x = -0.87133302 Simplifying x = -0.87133302Subproblem 2
x + 1.583333334 = -0.712000314 Simplifying x + 1.583333334 = -0.712000314 Reorder the terms: 1.583333334 + x = -0.712000314 Solving 1.583333334 + x = -0.712000314 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 = -0.712000314 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = -0.712000314 + -1.583333334 x = -0.712000314 + -1.583333334 Combine like terms: -0.712000314 + -1.583333334 = -2.295333648 x = -2.295333648 Simplifying x = -2.295333648Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.87133302, -2.295333648}
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