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Simplifying u2 + -14u = 43 Reorder the terms: -14u + u2 = 43 Solving -14u + u2 = 43 Solving for variable 'u'. Reorder the terms: -43 + -14u + u2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -14u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -14u + 43 + u2 = 0 + 43 Reorder the terms: -43 + 43 + -14u + u2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -14u + u2 = 0 + 43 -14u + u2 = 0 + 43 Combine like terms: 0 + 43 = 43 -14u + u2 = 43 The u term is -14u. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14u + 49 + u2 = 43 + 49 Reorder the terms: 49 + -14u + u2 = 43 + 49 Combine like terms: 43 + 49 = 92 49 + -14u + u2 = 92 Factor a perfect square on the left side: (u + -7)(u + -7) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (u + -7) equal to 9.591663047 and -9.591663047.Subproblem 1
u + -7 = 9.591663047 Simplifying u + -7 = 9.591663047 Reorder the terms: -7 + u = 9.591663047 Solving -7 + u = 9.591663047 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + u = 9.591663047 + 7 Combine like terms: -7 + 7 = 0 0 + u = 9.591663047 + 7 u = 9.591663047 + 7 Combine like terms: 9.591663047 + 7 = 16.591663047 u = 16.591663047 Simplifying u = 16.591663047Subproblem 2
u + -7 = -9.591663047 Simplifying u + -7 = -9.591663047 Reorder the terms: -7 + u = -9.591663047 Solving -7 + u = -9.591663047 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + u = -9.591663047 + 7 Combine like terms: -7 + 7 = 0 0 + u = -9.591663047 + 7 u = -9.591663047 + 7 Combine like terms: -9.591663047 + 7 = -2.591663047 u = -2.591663047 Simplifying u = -2.591663047Solution
The solution to the problem is based on the solutions from the subproblems. u = {16.591663047, -2.591663047}
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