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Simplifying 6u2 + -17u + -6 = 0 Reorder the terms: -6 + -17u + 6u2 = 0 Solving -6 + -17u + 6u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + -2.833333333u + u2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.833333333u + 1 + u2 = 0 + 1 Reorder the terms: -1 + 1 + -2.833333333u + u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.833333333u + u2 = 0 + 1 -2.833333333u + u2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.833333333u + u2 = 1 The u term is -2.833333333u. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333u + 2.006944445 + u2 = 1 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333u + u2 = 1 + 2.006944445 Combine like terms: 1 + 2.006944445 = 3.006944445 2.006944445 + -2.833333333u + u2 = 3.006944445 Factor a perfect square on the left side: (u + -1.416666667)(u + -1.416666667) = 3.006944445 Calculate the square root of the right side: 1.734054337 Break this problem into two subproblems by setting (u + -1.416666667) equal to 1.734054337 and -1.734054337.Subproblem 1
u + -1.416666667 = 1.734054337 Simplifying u + -1.416666667 = 1.734054337 Reorder the terms: -1.416666667 + u = 1.734054337 Solving -1.416666667 + u = 1.734054337 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + u = 1.734054337 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + u = 1.734054337 + 1.416666667 u = 1.734054337 + 1.416666667 Combine like terms: 1.734054337 + 1.416666667 = 3.150721004 u = 3.150721004 Simplifying u = 3.150721004Subproblem 2
u + -1.416666667 = -1.734054337 Simplifying u + -1.416666667 = -1.734054337 Reorder the terms: -1.416666667 + u = -1.734054337 Solving -1.416666667 + u = -1.734054337 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + u = -1.734054337 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + u = -1.734054337 + 1.416666667 u = -1.734054337 + 1.416666667 Combine like terms: -1.734054337 + 1.416666667 = -0.31738767 u = -0.31738767 Simplifying u = -0.31738767Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.150721004, -0.31738767}
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