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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 = 5.694444447 3.361111114 + 3.666666667x + x2 = 5.694444447 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 5.694444447 Calculate the square root of the right side: 2.386303511 Break this problem into two subproblems by setting (x + 1.833333334) equal to 2.386303511 and -2.386303511.Subproblem 1
x + 1.833333334 = 2.386303511 Simplifying x + 1.833333334 = 2.386303511 Reorder the terms: 1.833333334 + x = 2.386303511 Solving 1.833333334 + x = 2.386303511 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 = 2.386303511 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 2.386303511 + -1.833333334 x = 2.386303511 + -1.833333334 Combine like terms: 2.386303511 + -1.833333334 = 0.552970177 x = 0.552970177 Simplifying x = 0.552970177Subproblem 2
x + 1.833333334 = -2.386303511 Simplifying x + 1.833333334 = -2.386303511 Reorder the terms: 1.833333334 + x = -2.386303511 Solving 1.833333334 + x = -2.386303511 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 = -2.386303511 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -2.386303511 + -1.833333334 x = -2.386303511 + -1.833333334 Combine like terms: -2.386303511 + -1.833333334 = -4.219636845 x = -4.219636845 Simplifying x = -4.219636845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.552970177, -4.219636845}Solution
x = {0.552970177, -4.219636845}
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