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Simplifying 6x2 + -22x + 14 = 0 Reorder the terms: 14 + -22x + 6x2 = 0 Solving 14 + -22x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -11x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -11x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + -11x + 3x2 = 0 Solving 7 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -3.666666667x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -3.666666667x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + -2.333333333 -3.666666667x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -3.666666667x + x2 = -2.333333333 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 = -2.333333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -2.333333333 + 3.361111114 Combine like terms: -2.333333333 + 3.361111114 = 1.027777781 3.361111114 + -3.666666667x + x2 = 1.027777781 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 1.027777781 Calculate the square root of the right side: 1.013793757 Break this problem into two subproblems by setting (x + -1.833333334) equal to 1.013793757 and -1.013793757.Subproblem 1
x + -1.833333334 = 1.013793757 Simplifying x + -1.833333334 = 1.013793757 Reorder the terms: -1.833333334 + x = 1.013793757 Solving -1.833333334 + x = 1.013793757 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 = 1.013793757 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 1.013793757 + 1.833333334 x = 1.013793757 + 1.833333334 Combine like terms: 1.013793757 + 1.833333334 = 2.847127091 x = 2.847127091 Simplifying x = 2.847127091Subproblem 2
x + -1.833333334 = -1.013793757 Simplifying x + -1.833333334 = -1.013793757 Reorder the terms: -1.833333334 + x = -1.013793757 Solving -1.833333334 + x = -1.013793757 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 = -1.013793757 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -1.013793757 + 1.833333334 x = -1.013793757 + 1.833333334 Combine like terms: -1.013793757 + 1.833333334 = 0.819539577 x = 0.819539577 Simplifying x = 0.819539577Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.847127091, 0.819539577}Solution
x = {2.847127091, 0.819539577}
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