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Simplifying 6x2 + 22x + 6 = 0 Reorder the terms: 6 + 22x + 6x2 = 0 Solving 6 + 22x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 11x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 11x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + 11x + 3x2 = 0 Solving 3 + 11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3.666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.666666667x + x2 = 0 + -1 3.666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.666666667x + x2 = -1 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 = -1 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = -1 + 3.361111114 Combine like terms: -1 + 3.361111114 = 2.361111114 3.361111114 + 3.666666667x + x2 = 2.361111114 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 2.361111114 Calculate the square root of the right side: 1.536590744 Break this problem into two subproblems by setting (x + 1.833333334) equal to 1.536590744 and -1.536590744.Subproblem 1
x + 1.833333334 = 1.536590744 Simplifying x + 1.833333334 = 1.536590744 Reorder the terms: 1.833333334 + x = 1.536590744 Solving 1.833333334 + x = 1.536590744 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 = 1.536590744 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 1.536590744 + -1.833333334 x = 1.536590744 + -1.833333334 Combine like terms: 1.536590744 + -1.833333334 = -0.29674259 x = -0.29674259 Simplifying x = -0.29674259Subproblem 2
x + 1.833333334 = -1.536590744 Simplifying x + 1.833333334 = -1.536590744 Reorder the terms: 1.833333334 + x = -1.536590744 Solving 1.833333334 + x = -1.536590744 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 = -1.536590744 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -1.536590744 + -1.833333334 x = -1.536590744 + -1.833333334 Combine like terms: -1.536590744 + -1.833333334 = -3.369924078 x = -3.369924078 Simplifying x = -3.369924078Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.29674259, -3.369924078}Solution
x = {-0.29674259, -3.369924078}
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