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Simplifying 6u2 = 2u2 + 16u + 15 Reorder the terms: 6u2 = 15 + 16u + 2u2 Solving 6u2 = 15 + 16u + 2u2 Solving for variable 'u'. Reorder the terms: -15 + -16u + 6u2 + -2u2 = 15 + 16u + 2u2 + -15 + -16u + -2u2 Combine like terms: 6u2 + -2u2 = 4u2 -15 + -16u + 4u2 = 15 + 16u + 2u2 + -15 + -16u + -2u2 Reorder the terms: -15 + -16u + 4u2 = 15 + -15 + 16u + -16u + 2u2 + -2u2 Combine like terms: 15 + -15 = 0 -15 + -16u + 4u2 = 0 + 16u + -16u + 2u2 + -2u2 -15 + -16u + 4u2 = 16u + -16u + 2u2 + -2u2 Combine like terms: 16u + -16u = 0 -15 + -16u + 4u2 = 0 + 2u2 + -2u2 -15 + -16u + 4u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 -15 + -16u + 4u2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -4u + u2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -4u + 3.75 + u2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -4u + u2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -4u + u2 = 0 + 3.75 -4u + u2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -4u + u2 = 3.75 The u term is -4u. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4u + 4 + u2 = 3.75 + 4 Reorder the terms: 4 + -4u + u2 = 3.75 + 4 Combine like terms: 3.75 + 4 = 7.75 4 + -4u + u2 = 7.75 Factor a perfect square on the left side: (u + -2)(u + -2) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (u + -2) equal to 2.783882181 and -2.783882181.Subproblem 1
u + -2 = 2.783882181 Simplifying u + -2 = 2.783882181 Reorder the terms: -2 + u = 2.783882181 Solving -2 + u = 2.783882181 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + u = 2.783882181 + 2 Combine like terms: -2 + 2 = 0 0 + u = 2.783882181 + 2 u = 2.783882181 + 2 Combine like terms: 2.783882181 + 2 = 4.783882181 u = 4.783882181 Simplifying u = 4.783882181Subproblem 2
u + -2 = -2.783882181 Simplifying u + -2 = -2.783882181 Reorder the terms: -2 + u = -2.783882181 Solving -2 + u = -2.783882181 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + u = -2.783882181 + 2 Combine like terms: -2 + 2 = 0 0 + u = -2.783882181 + 2 u = -2.783882181 + 2 Combine like terms: -2.783882181 + 2 = -0.783882181 u = -0.783882181 Simplifying u = -0.783882181Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.783882181, -0.783882181}
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