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Simplifying 6x2 + 11x = 13 Reorder the terms: 11x + 6x2 = 13 Solving 11x + 6x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 11x + 6x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 11x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + 1.833333333x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + 1.833333333x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + 1.833333333x + x2 = 0 + 2.166666667 1.833333333x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 1.833333333x + x2 = 2.166666667 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 = 2.166666667 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 2.166666667 + 0.8402777775 Combine like terms: 2.166666667 + 0.8402777775 = 3.0069444445 0.8402777775 + 1.833333333x + x2 = 3.0069444445 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 3.0069444445 Calculate the square root of the right side: 1.734054337 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 1.734054337 and -1.734054337.Subproblem 1
x + 0.9166666665 = 1.734054337 Simplifying x + 0.9166666665 = 1.734054337 Reorder the terms: 0.9166666665 + x = 1.734054337 Solving 0.9166666665 + x = 1.734054337 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 = 1.734054337 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 1.734054337 + -0.9166666665 x = 1.734054337 + -0.9166666665 Combine like terms: 1.734054337 + -0.9166666665 = 0.8173876705 x = 0.8173876705 Simplifying x = 0.8173876705Subproblem 2
x + 0.9166666665 = -1.734054337 Simplifying x + 0.9166666665 = -1.734054337 Reorder the terms: 0.9166666665 + x = -1.734054337 Solving 0.9166666665 + x = -1.734054337 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 = -1.734054337 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -1.734054337 + -0.9166666665 x = -1.734054337 + -0.9166666665 Combine like terms: -1.734054337 + -0.9166666665 = -2.6507210035 x = -2.6507210035 Simplifying x = -2.6507210035Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8173876705, -2.6507210035}
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