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Simplifying 6x2 + -19x = 10 Reorder the terms: -19x + 6x2 = 10 Solving -19x + 6x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -19x + 6x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.666666667 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -3.166666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -3.166666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + 1.666666667 -3.166666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -3.166666667x + x2 = 1.666666667 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 = 1.666666667 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 1.666666667 + 2.506944447 Combine like terms: 1.666666667 + 2.506944447 = 4.173611114 2.506944447 + -3.166666667x + x2 = 4.173611114 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 4.173611114 Calculate the square root of the right side: 2.042941779 Break this problem into two subproblems by setting (x + -1.583333334) equal to 2.042941779 and -2.042941779.Subproblem 1
x + -1.583333334 = 2.042941779 Simplifying x + -1.583333334 = 2.042941779 Reorder the terms: -1.583333334 + x = 2.042941779 Solving -1.583333334 + x = 2.042941779 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 = 2.042941779 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 2.042941779 + 1.583333334 x = 2.042941779 + 1.583333334 Combine like terms: 2.042941779 + 1.583333334 = 3.626275113 x = 3.626275113 Simplifying x = 3.626275113Subproblem 2
x + -1.583333334 = -2.042941779 Simplifying x + -1.583333334 = -2.042941779 Reorder the terms: -1.583333334 + x = -2.042941779 Solving -1.583333334 + x = -2.042941779 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 = -2.042941779 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -2.042941779 + 1.583333334 x = -2.042941779 + 1.583333334 Combine like terms: -2.042941779 + 1.583333334 = -0.459608445 x = -0.459608445 Simplifying x = -0.459608445Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.626275113, -0.459608445}
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