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Simplifying 0 = u2 + -7u + 3 Reorder the terms: 0 = 3 + -7u + u2 Solving 0 = 3 + -7u + u2 Solving for variable 'u'. Combine like terms: 0 + -3 = -3 -3 + 7u + -1u2 = 3 + -7u + u2 + -3 + 7u + -1u2 Reorder the terms: -3 + 7u + -1u2 = 3 + -3 + -7u + 7u + u2 + -1u2 Combine like terms: 3 + -3 = 0 -3 + 7u + -1u2 = 0 + -7u + 7u + u2 + -1u2 -3 + 7u + -1u2 = -7u + 7u + u2 + -1u2 Combine like terms: -7u + 7u = 0 -3 + 7u + -1u2 = 0 + u2 + -1u2 -3 + 7u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -3 + 7u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -7u + u2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -7u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -7u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7u + u2 = 0 + -3 -7u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -7u + u2 = -3 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 = -3 + 12.25 Reorder the terms: 12.25 + -7u + u2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + -7u + u2 = 9.25 Factor a perfect square on the left side: (u + -3.5)(u + -3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (u + -3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
u + -3.5 = 3.041381265 Simplifying u + -3.5 = 3.041381265 Reorder the terms: -3.5 + u = 3.041381265 Solving -3.5 + u = 3.041381265 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 = 3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + u = 3.041381265 + 3.5 u = 3.041381265 + 3.5 Combine like terms: 3.041381265 + 3.5 = 6.541381265 u = 6.541381265 Simplifying u = 6.541381265Subproblem 2
u + -3.5 = -3.041381265 Simplifying u + -3.5 = -3.041381265 Reorder the terms: -3.5 + u = -3.041381265 Solving -3.5 + u = -3.041381265 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 = -3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + u = -3.041381265 + 3.5 u = -3.041381265 + 3.5 Combine like terms: -3.041381265 + 3.5 = 0.458618735 u = 0.458618735 Simplifying u = 0.458618735Solution
The solution to the problem is based on the solutions from the subproblems. u = {6.541381265, 0.458618735}
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