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Simplifying u6 + -14u3 + -1 = 0 Reorder the terms: -1 + -14u3 + u6 = 0 Solving -1 + -14u3 + u6 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -14u3 + 1 + u6 = 0 + 1 Reorder the terms: -1 + 1 + -14u3 + u6 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -14u3 + u6 = 0 + 1 -14u3 + u6 = 0 + 1 Combine like terms: 0 + 1 = 1 -14u3 + u6 = 1 The u term is -14u3. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14u3 + 49 + u6 = 1 + 49 Reorder the terms: 49 + -14u3 + u6 = 1 + 49 Combine like terms: 1 + 49 = 50 49 + -14u3 + u6 = 50 Factor a perfect square on the left side: (u3 + -7)(u3 + -7) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (u3 + -7) equal to 7.071067812 and -7.071067812.Subproblem 1
u3 + -7 = 7.071067812 Simplifying u3 + -7 = 7.071067812 Reorder the terms: -7 + u3 = 7.071067812 Solving -7 + u3 = 7.071067812 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 + u3 = 7.071067812 + 7 Combine like terms: -7 + 7 = 0 0 + u3 = 7.071067812 + 7 u3 = 7.071067812 + 7 Combine like terms: 7.071067812 + 7 = 14.071067812 u3 = 14.071067812 Simplifying u3 = 14.071067812 Reorder the terms: -14.071067812 + u3 = 14.071067812 + -14.071067812 Combine like terms: 14.071067812 + -14.071067812 = 0.000000000 -14.071067812 + u3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
u3 + -7 = -7.071067812 Simplifying u3 + -7 = -7.071067812 Reorder the terms: -7 + u3 = -7.071067812 Solving -7 + u3 = -7.071067812 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 + u3 = -7.071067812 + 7 Combine like terms: -7 + 7 = 0 0 + u3 = -7.071067812 + 7 u3 = -7.071067812 + 7 Combine like terms: -7.071067812 + 7 = -0.071067812 u3 = -0.071067812 Simplifying u3 = -0.071067812 Reorder the terms: 0.071067812 + u3 = -0.071067812 + 0.071067812 Combine like terms: -0.071067812 + 0.071067812 = 0.000000000 0.071067812 + u3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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