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Simplifying 6x2 + 11x = 5 Reorder the terms: 11x + 6x2 = 5 Solving 11x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 11x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 1.833333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 1.833333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 1.833333333x + x2 = 0 + 0.8333333333 1.833333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 1.833333333x + x2 = 0.8333333333 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 = 0.8333333333 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 0.8333333333 + 0.8402777775 Combine like terms: 0.8333333333 + 0.8402777775 = 1.6736111108 0.8402777775 + 1.833333333x + x2 = 1.6736111108 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 1.6736111108 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 1.293681225 and -1.293681225.Subproblem 1
x + 0.9166666665 = 1.293681225 Simplifying x + 0.9166666665 = 1.293681225 Reorder the terms: 0.9166666665 + x = 1.293681225 Solving 0.9166666665 + x = 1.293681225 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 = 1.293681225 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 1.293681225 + -0.9166666665 x = 1.293681225 + -0.9166666665 Combine like terms: 1.293681225 + -0.9166666665 = 0.3770145585 x = 0.3770145585 Simplifying x = 0.3770145585Subproblem 2
x + 0.9166666665 = -1.293681225 Simplifying x + 0.9166666665 = -1.293681225 Reorder the terms: 0.9166666665 + x = -1.293681225 Solving 0.9166666665 + x = -1.293681225 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 = -1.293681225 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -1.293681225 + -0.9166666665 x = -1.293681225 + -0.9166666665 Combine like terms: -1.293681225 + -0.9166666665 = -2.2103478915 x = -2.2103478915 Simplifying x = -2.2103478915Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3770145585, -2.2103478915}
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