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Simplifying 6x2 + -19x = 30 Reorder the terms: -19x + 6x2 = 30 Solving -19x + 6x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -19x + 6x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -3.166666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -3.166666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3.166666667x + x2 = 0 + 5 -3.166666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3.166666667x + x2 = 5 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 = 5 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 5 + 2.506944447 Combine like terms: 5 + 2.506944447 = 7.506944447 2.506944447 + -3.166666667x + x2 = 7.506944447 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 7.506944447 Calculate the square root of the right side: 2.739880371 Break this problem into two subproblems by setting (x + -1.583333334) equal to 2.739880371 and -2.739880371.Subproblem 1
x + -1.583333334 = 2.739880371 Simplifying x + -1.583333334 = 2.739880371 Reorder the terms: -1.583333334 + x = 2.739880371 Solving -1.583333334 + x = 2.739880371 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 = 2.739880371 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 2.739880371 + 1.583333334 x = 2.739880371 + 1.583333334 Combine like terms: 2.739880371 + 1.583333334 = 4.323213705 x = 4.323213705 Simplifying x = 4.323213705Subproblem 2
x + -1.583333334 = -2.739880371 Simplifying x + -1.583333334 = -2.739880371 Reorder the terms: -1.583333334 + x = -2.739880371 Solving -1.583333334 + x = -2.739880371 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 = -2.739880371 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -2.739880371 + 1.583333334 x = -2.739880371 + 1.583333334 Combine like terms: -2.739880371 + 1.583333334 = -1.156547037 x = -1.156547037 Simplifying x = -1.156547037Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.323213705, -1.156547037}
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