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Simplifying 12x2 + 38x + -5 = 0 Reorder the terms: -5 + 38x + 12x2 = 0 Solving -5 + 38x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + 3.166666667x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + 3.166666667x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + 3.166666667x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + 3.166666667x + x2 = 0 + 0.4166666667 3.166666667x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 3.166666667x + x2 = 0.4166666667 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 = 0.4166666667 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667x + x2 = 0.4166666667 + 2.506944447 Combine like terms: 0.4166666667 + 2.506944447 = 2.9236111137 2.506944447 + 3.166666667x + x2 = 2.9236111137 Factor a perfect square on the left side: (x + 1.583333334)(x + 1.583333334) = 2.9236111137 Calculate the square root of the right side: 1.709857045 Break this problem into two subproblems by setting (x + 1.583333334) equal to 1.709857045 and -1.709857045.Subproblem 1
x + 1.583333334 = 1.709857045 Simplifying x + 1.583333334 = 1.709857045 Reorder the terms: 1.583333334 + x = 1.709857045 Solving 1.583333334 + x = 1.709857045 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 = 1.709857045 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = 1.709857045 + -1.583333334 x = 1.709857045 + -1.583333334 Combine like terms: 1.709857045 + -1.583333334 = 0.126523711 x = 0.126523711 Simplifying x = 0.126523711Subproblem 2
x + 1.583333334 = -1.709857045 Simplifying x + 1.583333334 = -1.709857045 Reorder the terms: 1.583333334 + x = -1.709857045 Solving 1.583333334 + x = -1.709857045 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 = -1.709857045 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = -1.709857045 + -1.583333334 x = -1.709857045 + -1.583333334 Combine like terms: -1.709857045 + -1.583333334 = -3.293190379 x = -3.293190379 Simplifying x = -3.293190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.126523711, -3.293190379}
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