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Simplifying 4u2 + 28u + 43 = 0 Reorder the terms: 43 + 28u + 4u2 = 0 Solving 43 + 28u + 4u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10.75 + 7u + u2 = 0 Move the constant term to the right: Add '-10.75' to each side of the equation. 10.75 + 7u + -10.75 + u2 = 0 + -10.75 Reorder the terms: 10.75 + -10.75 + 7u + u2 = 0 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + 7u + u2 = 0 + -10.75 7u + u2 = 0 + -10.75 Combine like terms: 0 + -10.75 = -10.75 7u + u2 = -10.75 The u term is 7u. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7u + 12.25 + u2 = -10.75 + 12.25 Reorder the terms: 12.25 + 7u + u2 = -10.75 + 12.25 Combine like terms: -10.75 + 12.25 = 1.5 12.25 + 7u + u2 = 1.5 Factor a perfect square on the left side: (u + 3.5)(u + 3.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (u + 3.5) equal to 1.224744871 and -1.224744871.Subproblem 1
u + 3.5 = 1.224744871 Simplifying u + 3.5 = 1.224744871 Reorder the terms: 3.5 + u = 1.224744871 Solving 3.5 + u = 1.224744871 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + u = 1.224744871 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + u = 1.224744871 + -3.5 u = 1.224744871 + -3.5 Combine like terms: 1.224744871 + -3.5 = -2.275255129 u = -2.275255129 Simplifying u = -2.275255129Subproblem 2
u + 3.5 = -1.224744871 Simplifying u + 3.5 = -1.224744871 Reorder the terms: 3.5 + u = -1.224744871 Solving 3.5 + u = -1.224744871 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + u = -1.224744871 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + u = -1.224744871 + -3.5 u = -1.224744871 + -3.5 Combine like terms: -1.224744871 + -3.5 = -4.724744871 u = -4.724744871 Simplifying u = -4.724744871Solution
The solution to the problem is based on the solutions from the subproblems. u = {-2.275255129, -4.724744871}
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