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Simplifying 12x2 + -22x = -5 Reorder the terms: -22x + 12x2 = -5 Solving -22x + 12x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + -22x + 12x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -22x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + -1.833333333x + -0.4166666667 + x2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + -1.833333333x + x2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + -1.833333333x + x2 = 0 + -0.4166666667 -1.833333333x + x2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 -1.833333333x + x2 = -0.4166666667 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 = -0.4166666667 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = -0.4166666667 + 0.8402777775 Combine like terms: -0.4166666667 + 0.8402777775 = 0.4236111108 0.8402777775 + -1.833333333x + x2 = 0.4236111108 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 0.4236111108 Calculate the square root of the right side: 0.650854139 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 0.650854139 and -0.650854139.Subproblem 1
x + -0.9166666665 = 0.650854139 Simplifying x + -0.9166666665 = 0.650854139 Reorder the terms: -0.9166666665 + x = 0.650854139 Solving -0.9166666665 + x = 0.650854139 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 = 0.650854139 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 0.650854139 + 0.9166666665 x = 0.650854139 + 0.9166666665 Combine like terms: 0.650854139 + 0.9166666665 = 1.5675208055 x = 1.5675208055 Simplifying x = 1.5675208055Subproblem 2
x + -0.9166666665 = -0.650854139 Simplifying x + -0.9166666665 = -0.650854139 Reorder the terms: -0.9166666665 + x = -0.650854139 Solving -0.9166666665 + x = -0.650854139 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 = -0.650854139 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -0.650854139 + 0.9166666665 x = -0.650854139 + 0.9166666665 Combine like terms: -0.650854139 + 0.9166666665 = 0.2658125275 x = 0.2658125275 Simplifying x = 0.2658125275Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5675208055, 0.2658125275}
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