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Simplifying 6x2 + -22x + -12 = 0 Reorder the terms: -12 + -22x + 6x2 = 0 Solving -12 + -22x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -11x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -11x + 3x2)' equal to zero and attempt to solve: Simplifying -6 + -11x + 3x2 = 0 Solving -6 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.666666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -3.666666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.666666667x + x2 = 0 + 2 -3.666666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.666666667x + x2 = 2 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 2 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 2 + 3.361111114 Combine like terms: 2 + 3.361111114 = 5.361111114 3.361111114 + -3.666666667x + x2 = 5.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 5.361111114 Calculate the square root of the right side: 2.315407332 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.315407332 and -2.315407332.Subproblem 1
x + -1.833333334 = 2.315407332 Simplifying x + -1.833333334 = 2.315407332 Reorder the terms: -1.833333334 + x = 2.315407332 Solving -1.833333334 + x = 2.315407332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 2.315407332 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.315407332 + 1.833333334 x = 2.315407332 + 1.833333334 Combine like terms: 2.315407332 + 1.833333334 = 4.148740666 x = 4.148740666 Simplifying x = 4.148740666Subproblem 2
x + -1.833333334 = -2.315407332 Simplifying x + -1.833333334 = -2.315407332 Reorder the terms: -1.833333334 + x = -2.315407332 Solving -1.833333334 + x = -2.315407332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -2.315407332 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.315407332 + 1.833333334 x = -2.315407332 + 1.833333334 Combine like terms: -2.315407332 + 1.833333334 = -0.482073998 x = -0.482073998 Simplifying x = -0.482073998Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.148740666, -0.482073998}Solution
x = {4.148740666, -0.482073998}
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