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Simplifying 6u(2 + -1u) = -7 (2 * 6u + -1u * 6u) = -7 (12u + -6u2) = -7 Solving 12u + -6u2 = -7 Solving for variable 'u'. Reorder the terms: 7 + 12u + -6u2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 12u + -6u2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.166666667 + -2u + u2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -2u + 1.166666667 + u2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -2u + u2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -2u + u2 = 0 + 1.166666667 -2u + u2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -2u + u2 = 1.166666667 The u term is -2u. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2u + 1 + u2 = 1.166666667 + 1 Reorder the terms: 1 + -2u + u2 = 1.166666667 + 1 Combine like terms: 1.166666667 + 1 = 2.166666667 1 + -2u + u2 = 2.166666667 Factor a perfect square on the left side: (u + -1)(u + -1) = 2.166666667 Calculate the square root of the right side: 1.471960145 Break this problem into two subproblems by setting (u + -1) equal to 1.471960145 and -1.471960145.Subproblem 1
u + -1 = 1.471960145 Simplifying u + -1 = 1.471960145 Reorder the terms: -1 + u = 1.471960145 Solving -1 + u = 1.471960145 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = 1.471960145 + 1 Combine like terms: -1 + 1 = 0 0 + u = 1.471960145 + 1 u = 1.471960145 + 1 Combine like terms: 1.471960145 + 1 = 2.471960145 u = 2.471960145 Simplifying u = 2.471960145Subproblem 2
u + -1 = -1.471960145 Simplifying u + -1 = -1.471960145 Reorder the terms: -1 + u = -1.471960145 Solving -1 + u = -1.471960145 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u = -1.471960145 + 1 Combine like terms: -1 + 1 = 0 0 + u = -1.471960145 + 1 u = -1.471960145 + 1 Combine like terms: -1.471960145 + 1 = -0.471960145 u = -0.471960145 Simplifying u = -0.471960145Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.471960145, -0.471960145}
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