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Simplifying 6x2 + 16x + 6 = 0 Reorder the terms: 6 + 16x + 6x2 = 0 Solving 6 + 16x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 8x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + 8x + 3x2 = 0 Solving 3 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.666666667x + x2 = 0 + -1 2.666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.666666667x + x2 = -1 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -1 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -1 + 1.777777780 Combine like terms: -1 + 1.777777780 = 0.77777778 1.777777780 + 2.666666667x + x2 = 0.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 0.77777778 Calculate the square root of the right side: 0.881917105 Break this problem into two subproblems by setting (x + 1.333333334) equal to 0.881917105 and -0.881917105.Subproblem 1
x + 1.333333334 = 0.881917105 Simplifying x + 1.333333334 = 0.881917105 Reorder the terms: 1.333333334 + x = 0.881917105 Solving 1.333333334 + x = 0.881917105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 0.881917105 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 0.881917105 + -1.333333334 x = 0.881917105 + -1.333333334 Combine like terms: 0.881917105 + -1.333333334 = -0.451416229 x = -0.451416229 Simplifying x = -0.451416229Subproblem 2
x + 1.333333334 = -0.881917105 Simplifying x + 1.333333334 = -0.881917105 Reorder the terms: 1.333333334 + x = -0.881917105 Solving 1.333333334 + x = -0.881917105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -0.881917105 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -0.881917105 + -1.333333334 x = -0.881917105 + -1.333333334 Combine like terms: -0.881917105 + -1.333333334 = -2.215250439 x = -2.215250439 Simplifying x = -2.215250439Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.451416229, -2.215250439}Solution
x = {-0.451416229, -2.215250439}
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