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Simplifying 6x2 + -19x + -3 = 0 Reorder the terms: -3 + -19x + 6x2 = 0 Solving -3 + -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'. -0.5 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.166666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.166666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.166666667x + x2 = 0 + 0.5 -3.166666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.166666667x + x2 = 0.5 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 = 0.5 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 0.5 + 2.506944447 Combine like terms: 0.5 + 2.506944447 = 3.006944447 2.506944447 + -3.166666667x + x2 = 3.006944447 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 3.006944447 Calculate the square root of the right side: 1.734054338 Break this problem into two subproblems by setting (x + -1.583333334) equal to 1.734054338 and -1.734054338.Subproblem 1
x + -1.583333334 = 1.734054338 Simplifying x + -1.583333334 = 1.734054338 Reorder the terms: -1.583333334 + x = 1.734054338 Solving -1.583333334 + x = 1.734054338 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 = 1.734054338 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 1.734054338 + 1.583333334 x = 1.734054338 + 1.583333334 Combine like terms: 1.734054338 + 1.583333334 = 3.317387672 x = 3.317387672 Simplifying x = 3.317387672Subproblem 2
x + -1.583333334 = -1.734054338 Simplifying x + -1.583333334 = -1.734054338 Reorder the terms: -1.583333334 + x = -1.734054338 Solving -1.583333334 + x = -1.734054338 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 = -1.734054338 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -1.734054338 + 1.583333334 x = -1.734054338 + 1.583333334 Combine like terms: -1.734054338 + 1.583333334 = -0.150721004 x = -0.150721004 Simplifying x = -0.150721004Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.317387672, -0.150721004}
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