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Simplifying 2u2 + 9u = 19 Reorder the terms: 9u + 2u2 = 19 Solving 9u + 2u2 = 19 Solving for variable 'u'. Reorder the terms: -19 + 9u + 2u2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 9u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 4.5u + u2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 4.5u + 9.5 + u2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 4.5u + u2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 4.5u + u2 = 0 + 9.5 4.5u + u2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 4.5u + u2 = 9.5 The u term is 4.5u. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5u + 5.0625 + u2 = 9.5 + 5.0625 Reorder the terms: 5.0625 + 4.5u + u2 = 9.5 + 5.0625 Combine like terms: 9.5 + 5.0625 = 14.5625 5.0625 + 4.5u + u2 = 14.5625 Factor a perfect square on the left side: (u + 2.25)(u + 2.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (u + 2.25) equal to 3.816084381 and -3.816084381.Subproblem 1
u + 2.25 = 3.816084381 Simplifying u + 2.25 = 3.816084381 Reorder the terms: 2.25 + u = 3.816084381 Solving 2.25 + u = 3.816084381 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + u = 3.816084381 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + u = 3.816084381 + -2.25 u = 3.816084381 + -2.25 Combine like terms: 3.816084381 + -2.25 = 1.566084381 u = 1.566084381 Simplifying u = 1.566084381Subproblem 2
u + 2.25 = -3.816084381 Simplifying u + 2.25 = -3.816084381 Reorder the terms: 2.25 + u = -3.816084381 Solving 2.25 + u = -3.816084381 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + u = -3.816084381 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + u = -3.816084381 + -2.25 u = -3.816084381 + -2.25 Combine like terms: -3.816084381 + -2.25 = -6.066084381 u = -6.066084381 Simplifying u = -6.066084381Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.566084381, -6.066084381}
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