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Simplifying 2u2 + -8u + 9 = u2 + 1 Reorder the terms: 9 + -8u + 2u2 = u2 + 1 Reorder the terms: 9 + -8u + 2u2 = 1 + u2 Solving 9 + -8u + 2u2 = 1 + u2 Solving for variable 'u'. Reorder the terms: 9 + -1 + -8u + 2u2 + -1u2 = 1 + u2 + -1 + -1u2 Combine like terms: 9 + -1 = 8 8 + -8u + 2u2 + -1u2 = 1 + u2 + -1 + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 8 + -8u + 1u2 = 1 + u2 + -1 + -1u2 Reorder the terms: 8 + -8u + 1u2 = 1 + -1 + u2 + -1u2 Combine like terms: 1 + -1 = 0 8 + -8u + 1u2 = 0 + u2 + -1u2 8 + -8u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 8 + -8u + 1u2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -8u + -8 + u2 = 0 + -8 Reorder the terms: 8 + -8 + -8u + u2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -8u + u2 = 0 + -8 -8u + u2 = 0 + -8 Combine like terms: 0 + -8 = -8 -8u + u2 = -8 The u term is -8u. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8u + 16 + u2 = -8 + 16 Reorder the terms: 16 + -8u + u2 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + -8u + u2 = 8 Factor a perfect square on the left side: (u + -4)(u + -4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (u + -4) equal to 2.828427125 and -2.828427125.Subproblem 1
u + -4 = 2.828427125 Simplifying u + -4 = 2.828427125 Reorder the terms: -4 + u = 2.828427125 Solving -4 + u = 2.828427125 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = 2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + u = 2.828427125 + 4 u = 2.828427125 + 4 Combine like terms: 2.828427125 + 4 = 6.828427125 u = 6.828427125 Simplifying u = 6.828427125Subproblem 2
u + -4 = -2.828427125 Simplifying u + -4 = -2.828427125 Reorder the terms: -4 + u = -2.828427125 Solving -4 + u = -2.828427125 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = -2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + u = -2.828427125 + 4 u = -2.828427125 + 4 Combine like terms: -2.828427125 + 4 = 1.171572875 u = 1.171572875 Simplifying u = 1.171572875Solution
The solution to the problem is based on the solutions from the subproblems. u = {6.828427125, 1.171572875}
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