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Simplifying u2 + -7u + 9 = 0 Reorder the terms: 9 + -7u + u2 = 0 Solving 9 + -7u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -7u + -9 + u2 = 0 + -9 Reorder the terms: 9 + -9 + -7u + u2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7u + u2 = 0 + -9 -7u + u2 = 0 + -9 Combine like terms: 0 + -9 = -9 -7u + u2 = -9 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 = -9 + 12.25 Reorder the terms: 12.25 + -7u + u2 = -9 + 12.25 Combine like terms: -9 + 12.25 = 3.25 12.25 + -7u + u2 = 3.25 Factor a perfect square on the left side: (u + -3.5)(u + -3.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (u + -3.5) equal to 1.802775638 and -1.802775638.Subproblem 1
u + -3.5 = 1.802775638 Simplifying u + -3.5 = 1.802775638 Reorder the terms: -3.5 + u = 1.802775638 Solving -3.5 + u = 1.802775638 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 = 1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + u = 1.802775638 + 3.5 u = 1.802775638 + 3.5 Combine like terms: 1.802775638 + 3.5 = 5.302775638 u = 5.302775638 Simplifying u = 5.302775638Subproblem 2
u + -3.5 = -1.802775638 Simplifying u + -3.5 = -1.802775638 Reorder the terms: -3.5 + u = -1.802775638 Solving -3.5 + u = -1.802775638 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 = -1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + u = -1.802775638 + 3.5 u = -1.802775638 + 3.5 Combine like terms: -1.802775638 + 3.5 = 1.697224362 u = 1.697224362 Simplifying u = 1.697224362Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.302775638, 1.697224362}
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