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Simplifying 12u2 + -13u + -6 = 0 Reorder the terms: -6 + -13u + 12u2 = 0 Solving -6 + -13u + 12u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5 + -1.083333333u + u2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.083333333u + 0.5 + u2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.083333333u + u2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.083333333u + u2 = 0 + 0.5 -1.083333333u + u2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.083333333u + u2 = 0.5 The u term is -1.083333333u. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333u + 0.2934027776 + u2 = 0.5 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333u + u2 = 0.5 + 0.2934027776 Combine like terms: 0.5 + 0.2934027776 = 0.7934027776 0.2934027776 + -1.083333333u + u2 = 0.7934027776 Factor a perfect square on the left side: (u + -0.5416666665)(u + -0.5416666665) = 0.7934027776 Calculate the square root of the right side: 0.890731597 Break this problem into two subproblems by setting (u + -0.5416666665) equal to 0.890731597 and -0.890731597.Subproblem 1
u + -0.5416666665 = 0.890731597 Simplifying u + -0.5416666665 = 0.890731597 Reorder the terms: -0.5416666665 + u = 0.890731597 Solving -0.5416666665 + u = 0.890731597 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + u = 0.890731597 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + u = 0.890731597 + 0.5416666665 u = 0.890731597 + 0.5416666665 Combine like terms: 0.890731597 + 0.5416666665 = 1.4323982635 u = 1.4323982635 Simplifying u = 1.4323982635Subproblem 2
u + -0.5416666665 = -0.890731597 Simplifying u + -0.5416666665 = -0.890731597 Reorder the terms: -0.5416666665 + u = -0.890731597 Solving -0.5416666665 + u = -0.890731597 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + u = -0.890731597 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + u = -0.890731597 + 0.5416666665 u = -0.890731597 + 0.5416666665 Combine like terms: -0.890731597 + 0.5416666665 = -0.3490649305 u = -0.3490649305 Simplifying u = -0.3490649305Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.4323982635, -0.3490649305}
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