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Simplifying 12x2 + -26x + -8 = 0 Reorder the terms: -8 + -26x + 12x2 = 0 Solving -8 + -26x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -13x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -13x + 6x2)' equal to zero and attempt to solve: Simplifying -4 + -13x + 6x2 = 0 Solving -4 + -13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.6666666667 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -2.166666667x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -2.166666667x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -2.166666667x + x2 = 0 + 0.6666666667 -2.166666667x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -2.166666667x + x2 = 0.6666666667 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = 0.6666666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 0.6666666667 + 1.173611113 Combine like terms: 0.6666666667 + 1.173611113 = 1.8402777797 1.173611113 + -2.166666667x + x2 = 1.8402777797 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 1.8402777797 Calculate the square root of the right side: 1.356568384 Break this problem into two subproblems by setting (x + -1.083333334) equal to 1.356568384 and -1.356568384.Subproblem 1
x + -1.083333334 = 1.356568384 Simplifying x + -1.083333334 = 1.356568384 Reorder the terms: -1.083333334 + x = 1.356568384 Solving -1.083333334 + x = 1.356568384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 1.356568384 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.356568384 + 1.083333334 x = 1.356568384 + 1.083333334 Combine like terms: 1.356568384 + 1.083333334 = 2.439901718 x = 2.439901718 Simplifying x = 2.439901718Subproblem 2
x + -1.083333334 = -1.356568384 Simplifying x + -1.083333334 = -1.356568384 Reorder the terms: -1.083333334 + x = -1.356568384 Solving -1.083333334 + x = -1.356568384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -1.356568384 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.356568384 + 1.083333334 x = -1.356568384 + 1.083333334 Combine like terms: -1.356568384 + 1.083333334 = -0.27323505 x = -0.27323505 Simplifying x = -0.27323505Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.439901718, -0.27323505}Solution
x = {2.439901718, -0.27323505}
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