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Simplifying u2 + 19u = -12 Reorder the terms: 19u + u2 = -12 Solving 19u + u2 = -12 Solving for variable 'u'. Reorder the terms: 12 + 19u + u2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + 19u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 19u + -12 + u2 = 0 + -12 Reorder the terms: 12 + -12 + 19u + u2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 19u + u2 = 0 + -12 19u + u2 = 0 + -12 Combine like terms: 0 + -12 = -12 19u + u2 = -12 The u term is 19u. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19u + 90.25 + u2 = -12 + 90.25 Reorder the terms: 90.25 + 19u + u2 = -12 + 90.25 Combine like terms: -12 + 90.25 = 78.25 90.25 + 19u + u2 = 78.25 Factor a perfect square on the left side: (u + 9.5)(u + 9.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (u + 9.5) equal to 8.845903006 and -8.845903006.Subproblem 1
u + 9.5 = 8.845903006 Simplifying u + 9.5 = 8.845903006 Reorder the terms: 9.5 + u = 8.845903006 Solving 9.5 + u = 8.845903006 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + u = 8.845903006 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + u = 8.845903006 + -9.5 u = 8.845903006 + -9.5 Combine like terms: 8.845903006 + -9.5 = -0.654096994 u = -0.654096994 Simplifying u = -0.654096994Subproblem 2
u + 9.5 = -8.845903006 Simplifying u + 9.5 = -8.845903006 Reorder the terms: 9.5 + u = -8.845903006 Solving 9.5 + u = -8.845903006 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + u = -8.845903006 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + u = -8.845903006 + -9.5 u = -8.845903006 + -9.5 Combine like terms: -8.845903006 + -9.5 = -18.345903006 u = -18.345903006 Simplifying u = -18.345903006Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.654096994, -18.345903006}
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