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Simplifying 6u2 + -9u = 1.5 Reorder the terms: -9u + 6u2 = 1.5 Solving -9u + 6u2 = 1.5 Solving for variable 'u'. Reorder the terms: -1.5 + -9u + 6u2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + -9u + 6u2 = 0.0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.25 + -1.5u + u2 = 0.0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.5u + 0.25 + u2 = 0.0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.5u + u2 = 0.0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.5u + u2 = 0.0 + 0.25 -1.5u + u2 = 0.0 + 0.25 Combine like terms: 0.0 + 0.25 = 0.25 -1.5u + u2 = 0.25 The u term is -1.5u. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5u + 0.5625 + u2 = 0.25 + 0.5625 Reorder the terms: 0.5625 + -1.5u + u2 = 0.25 + 0.5625 Combine like terms: 0.25 + 0.5625 = 0.8125 0.5625 + -1.5u + u2 = 0.8125 Factor a perfect square on the left side: (u + -0.75)(u + -0.75) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (u + -0.75) equal to 0.901387819 and -0.901387819.Subproblem 1
u + -0.75 = 0.901387819 Simplifying u + -0.75 = 0.901387819 Reorder the terms: -0.75 + u = 0.901387819 Solving -0.75 + u = 0.901387819 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + u = 0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + u = 0.901387819 + 0.75 u = 0.901387819 + 0.75 Combine like terms: 0.901387819 + 0.75 = 1.651387819 u = 1.651387819 Simplifying u = 1.651387819Subproblem 2
u + -0.75 = -0.901387819 Simplifying u + -0.75 = -0.901387819 Reorder the terms: -0.75 + u = -0.901387819 Solving -0.75 + u = -0.901387819 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + u = -0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + u = -0.901387819 + 0.75 u = -0.901387819 + 0.75 Combine like terms: -0.901387819 + 0.75 = -0.151387819 u = -0.151387819 Simplifying u = -0.151387819Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.651387819, -0.151387819}
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