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Simplifying 3(u + -3) * 4u = 11 Reorder the terms: 3(-3 + u) * 4u = 11 Reorder the terms for easier multiplication: 3 * 4u(-3 + u) = 11 Multiply 3 * 4 12u(-3 + u) = 11 (-3 * 12u + u * 12u) = 11 (-36u + 12u2) = 11 Solving -36u + 12u2 = 11 Solving for variable 'u'. Reorder the terms: -11 + -36u + 12u2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -36u + 12u2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.9166666667 + -3u + u2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -3u + 0.9166666667 + u2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -3u + u2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -3u + u2 = 0 + 0.9166666667 -3u + u2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -3u + u2 = 0.9166666667 The u term is -3u. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3u + 2.25 + u2 = 0.9166666667 + 2.25 Reorder the terms: 2.25 + -3u + u2 = 0.9166666667 + 2.25 Combine like terms: 0.9166666667 + 2.25 = 3.1666666667 2.25 + -3u + u2 = 3.1666666667 Factor a perfect square on the left side: (u + -1.5)(u + -1.5) = 3.1666666667 Calculate the square root of the right side: 1.779513042 Break this problem into two subproblems by setting (u + -1.5) equal to 1.779513042 and -1.779513042.Subproblem 1
u + -1.5 = 1.779513042 Simplifying u + -1.5 = 1.779513042 Reorder the terms: -1.5 + u = 1.779513042 Solving -1.5 + u = 1.779513042 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + u = 1.779513042 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + u = 1.779513042 + 1.5 u = 1.779513042 + 1.5 Combine like terms: 1.779513042 + 1.5 = 3.279513042 u = 3.279513042 Simplifying u = 3.279513042Subproblem 2
u + -1.5 = -1.779513042 Simplifying u + -1.5 = -1.779513042 Reorder the terms: -1.5 + u = -1.779513042 Solving -1.5 + u = -1.779513042 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + u = -1.779513042 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + u = -1.779513042 + 1.5 u = -1.779513042 + 1.5 Combine like terms: -1.779513042 + 1.5 = -0.279513042 u = -0.279513042 Simplifying u = -0.279513042Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.279513042, -0.279513042}
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