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Simplifying (2u2 + -5u + 6) + (-3u2 + 7u + 1) = 0 Reorder the terms: (6 + -5u + 2u2) + (-3u2 + 7u + 1) = 0 Remove parenthesis around (6 + -5u + 2u2) 6 + -5u + 2u2 + (-3u2 + 7u + 1) = 0 Reorder the terms: 6 + -5u + 2u2 + (1 + 7u + -3u2) = 0 Remove parenthesis around (1 + 7u + -3u2) 6 + -5u + 2u2 + 1 + 7u + -3u2 = 0 Reorder the terms: 6 + 1 + -5u + 7u + 2u2 + -3u2 = 0 Combine like terms: 6 + 1 = 7 7 + -5u + 7u + 2u2 + -3u2 = 0 Combine like terms: -5u + 7u = 2u 7 + 2u + 2u2 + -3u2 = 0 Combine like terms: 2u2 + -3u2 = -1u2 7 + 2u + -1u2 = 0 Solving 7 + 2u + -1u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -2u + u2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -2u + 7 + u2 = 0 + 7 Reorder the terms: -7 + 7 + -2u + u2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2u + u2 = 0 + 7 -2u + u2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2u + u2 = 7 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 = 7 + 1 Reorder the terms: 1 + -2u + u2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2u + u2 = 8 Factor a perfect square on the left side: (u + -1)(u + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (u + -1) equal to 2.828427125 and -2.828427125.Subproblem 1
u + -1 = 2.828427125 Simplifying u + -1 = 2.828427125 Reorder the terms: -1 + u = 2.828427125 Solving -1 + u = 2.828427125 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 = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + u = 2.828427125 + 1 u = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 u = 3.828427125 Simplifying u = 3.828427125Subproblem 2
u + -1 = -2.828427125 Simplifying u + -1 = -2.828427125 Reorder the terms: -1 + u = -2.828427125 Solving -1 + u = -2.828427125 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 = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + u = -2.828427125 + 1 u = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 u = -1.828427125 Simplifying u = -1.828427125Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.828427125, -1.828427125}
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