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Simplifying 2u2 + -6u + -20 = u2 + 4 Reorder the terms: -20 + -6u + 2u2 = u2 + 4 Reorder the terms: -20 + -6u + 2u2 = 4 + u2 Solving -20 + -6u + 2u2 = 4 + u2 Solving for variable 'u'. Reorder the terms: -20 + -4 + -6u + 2u2 + -1u2 = 4 + u2 + -4 + -1u2 Combine like terms: -20 + -4 = -24 -24 + -6u + 2u2 + -1u2 = 4 + u2 + -4 + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 -24 + -6u + 1u2 = 4 + u2 + -4 + -1u2 Reorder the terms: -24 + -6u + 1u2 = 4 + -4 + u2 + -1u2 Combine like terms: 4 + -4 = 0 -24 + -6u + 1u2 = 0 + u2 + -1u2 -24 + -6u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -24 + -6u + 1u2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -6u + 24 + u2 = 0 + 24 Reorder the terms: -24 + 24 + -6u + u2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -6u + u2 = 0 + 24 -6u + u2 = 0 + 24 Combine like terms: 0 + 24 = 24 -6u + u2 = 24 The u term is -6u. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6u + 9 + u2 = 24 + 9 Reorder the terms: 9 + -6u + u2 = 24 + 9 Combine like terms: 24 + 9 = 33 9 + -6u + u2 = 33 Factor a perfect square on the left side: (u + -3)(u + -3) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (u + -3) equal to 5.744562647 and -5.744562647.Subproblem 1
u + -3 = 5.744562647 Simplifying u + -3 = 5.744562647 Reorder the terms: -3 + u = 5.744562647 Solving -3 + u = 5.744562647 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = 5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + u = 5.744562647 + 3 u = 5.744562647 + 3 Combine like terms: 5.744562647 + 3 = 8.744562647 u = 8.744562647 Simplifying u = 8.744562647Subproblem 2
u + -3 = -5.744562647 Simplifying u + -3 = -5.744562647 Reorder the terms: -3 + u = -5.744562647 Solving -3 + u = -5.744562647 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = -5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + u = -5.744562647 + 3 u = -5.744562647 + 3 Combine like terms: -5.744562647 + 3 = -2.744562647 u = -2.744562647 Simplifying u = -2.744562647Solution
The solution to the problem is based on the solutions from the subproblems. u = {8.744562647, -2.744562647}
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