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Simplifying 4u2 = 8u + 1 Reorder the terms: 4u2 = 1 + 8u Solving 4u2 = 1 + 8u Solving for variable 'u'. Reorder the terms: -1 + -8u + 4u2 = 1 + 8u + -1 + -8u Reorder the terms: -1 + -8u + 4u2 = 1 + -1 + 8u + -8u Combine like terms: 1 + -1 = 0 -1 + -8u + 4u2 = 0 + 8u + -8u -1 + -8u + 4u2 = 8u + -8u Combine like terms: 8u + -8u = 0 -1 + -8u + 4u2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -2u + u2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2u + 0.25 + u2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2u + u2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2u + u2 = 0 + 0.25 -2u + u2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2u + u2 = 0.25 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 = 0.25 + 1 Reorder the terms: 1 + -2u + u2 = 0.25 + 1 Combine like terms: 0.25 + 1 = 1.25 1 + -2u + u2 = 1.25 Factor a perfect square on the left side: (u + -1)(u + -1) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (u + -1) equal to 1.118033989 and -1.118033989.Subproblem 1
u + -1 = 1.118033989 Simplifying u + -1 = 1.118033989 Reorder the terms: -1 + u = 1.118033989 Solving -1 + u = 1.118033989 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 = 1.118033989 + 1 Combine like terms: -1 + 1 = 0 0 + u = 1.118033989 + 1 u = 1.118033989 + 1 Combine like terms: 1.118033989 + 1 = 2.118033989 u = 2.118033989 Simplifying u = 2.118033989Subproblem 2
u + -1 = -1.118033989 Simplifying u + -1 = -1.118033989 Reorder the terms: -1 + u = -1.118033989 Solving -1 + u = -1.118033989 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 = -1.118033989 + 1 Combine like terms: -1 + 1 = 0 0 + u = -1.118033989 + 1 u = -1.118033989 + 1 Combine like terms: -1.118033989 + 1 = -0.118033989 u = -0.118033989 Simplifying u = -0.118033989Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.118033989, -0.118033989}
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