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Simplifying 2u2 + 14u + -21 = 0 Reorder the terms: -21 + 14u + 2u2 = 0 Solving -21 + 14u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 7u + u2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 7u + 10.5 + u2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 7u + u2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 7u + u2 = 0 + 10.5 7u + u2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 7u + u2 = 10.5 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 = 10.5 + 12.25 Reorder the terms: 12.25 + 7u + u2 = 10.5 + 12.25 Combine like terms: 10.5 + 12.25 = 22.75 12.25 + 7u + u2 = 22.75 Factor a perfect square on the left side: (u + 3.5)(u + 3.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (u + 3.5) equal to 4.769696007 and -4.769696007.Subproblem 1
u + 3.5 = 4.769696007 Simplifying u + 3.5 = 4.769696007 Reorder the terms: 3.5 + u = 4.769696007 Solving 3.5 + u = 4.769696007 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 = 4.769696007 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + u = 4.769696007 + -3.5 u = 4.769696007 + -3.5 Combine like terms: 4.769696007 + -3.5 = 1.269696007 u = 1.269696007 Simplifying u = 1.269696007Subproblem 2
u + 3.5 = -4.769696007 Simplifying u + 3.5 = -4.769696007 Reorder the terms: 3.5 + u = -4.769696007 Solving 3.5 + u = -4.769696007 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 = -4.769696007 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + u = -4.769696007 + -3.5 u = -4.769696007 + -3.5 Combine like terms: -4.769696007 + -3.5 = -8.269696007 u = -8.269696007 Simplifying u = -8.269696007Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.269696007, -8.269696007}
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