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Simplifying 4(6x2 + 11x) + -2 = 0 Reorder the terms: 4(11x + 6x2) + -2 = 0 (11x * 4 + 6x2 * 4) + -2 = 0 (44x + 24x2) + -2 = 0 Reorder the terms: -2 + 44x + 24x2 = 0 Solving -2 + 44x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 22x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 22x + 12x2)' equal to zero and attempt to solve: Simplifying -1 + 22x + 12x2 = 0 Solving -1 + 22x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 1.833333333x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 1.833333333x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 1.833333333x + x2 = 0 + 0.08333333333 1.833333333x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 1.833333333x + x2 = 0.08333333333 The x term is 1.833333333x. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333x + 0.8402777775 + x2 = 0.08333333333 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 0.08333333333 + 0.8402777775 Combine like terms: 0.08333333333 + 0.8402777775 = 0.92361111083 0.8402777775 + 1.833333333x + x2 = 0.92361111083 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 0.92361111083 Calculate the square root of the right side: 0.961046883 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 0.961046883 and -0.961046883.Subproblem 1
x + 0.9166666665 = 0.961046883 Simplifying x + 0.9166666665 = 0.961046883 Reorder the terms: 0.9166666665 + x = 0.961046883 Solving 0.9166666665 + x = 0.961046883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = 0.961046883 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 0.961046883 + -0.9166666665 x = 0.961046883 + -0.9166666665 Combine like terms: 0.961046883 + -0.9166666665 = 0.0443802165 x = 0.0443802165 Simplifying x = 0.0443802165Subproblem 2
x + 0.9166666665 = -0.961046883 Simplifying x + 0.9166666665 = -0.961046883 Reorder the terms: 0.9166666665 + x = -0.961046883 Solving 0.9166666665 + x = -0.961046883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = -0.961046883 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -0.961046883 + -0.9166666665 x = -0.961046883 + -0.9166666665 Combine like terms: -0.961046883 + -0.9166666665 = -1.8777135495 x = -1.8777135495 Simplifying x = -1.8777135495Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0443802165, -1.8777135495}Solution
x = {0.0443802165, -1.8777135495}
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