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Simplifying u2 + -8u + -27 = 0 Reorder the terms: -27 + -8u + u2 = 0 Solving -27 + -8u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -8u + 27 + u2 = 0 + 27 Reorder the terms: -27 + 27 + -8u + u2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -8u + u2 = 0 + 27 -8u + u2 = 0 + 27 Combine like terms: 0 + 27 = 27 -8u + u2 = 27 The u term is -8u. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8u + 16 + u2 = 27 + 16 Reorder the terms: 16 + -8u + u2 = 27 + 16 Combine like terms: 27 + 16 = 43 16 + -8u + u2 = 43 Factor a perfect square on the left side: (u + -4)(u + -4) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (u + -4) equal to 6.557438524 and -6.557438524.Subproblem 1
u + -4 = 6.557438524 Simplifying u + -4 = 6.557438524 Reorder the terms: -4 + u = 6.557438524 Solving -4 + u = 6.557438524 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = 6.557438524 + 4 Combine like terms: -4 + 4 = 0 0 + u = 6.557438524 + 4 u = 6.557438524 + 4 Combine like terms: 6.557438524 + 4 = 10.557438524 u = 10.557438524 Simplifying u = 10.557438524Subproblem 2
u + -4 = -6.557438524 Simplifying u + -4 = -6.557438524 Reorder the terms: -4 + u = -6.557438524 Solving -4 + u = -6.557438524 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + u = -6.557438524 + 4 Combine like terms: -4 + 4 = 0 0 + u = -6.557438524 + 4 u = -6.557438524 + 4 Combine like terms: -6.557438524 + 4 = -2.557438524 u = -2.557438524 Simplifying u = -2.557438524Solution
The solution to the problem is based on the solutions from the subproblems. u = {10.557438524, -2.557438524}
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