u^2-34u+102=0

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Solution for u^2-34u+102=0 equation:


Simplifying
u2 + -34u + 102 = 0

Reorder the terms:
102 + -34u + u2 = 0

Solving
102 + -34u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-102' to each side of the equation.
102 + -34u + -102 + u2 = 0 + -102

Reorder the terms:
102 + -102 + -34u + u2 = 0 + -102

Combine like terms: 102 + -102 = 0
0 + -34u + u2 = 0 + -102
-34u + u2 = 0 + -102

Combine like terms: 0 + -102 = -102
-34u + u2 = -102

The u term is -34u.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34u + 289 + u2 = -102 + 289

Reorder the terms:
289 + -34u + u2 = -102 + 289

Combine like terms: -102 + 289 = 187
289 + -34u + u2 = 187

Factor a perfect square on the left side:
(u + -17)(u + -17) = 187

Calculate the square root of the right side: 13.674794331

Break this problem into two subproblems by setting 
(u + -17) equal to 13.674794331 and -13.674794331.

Subproblem 1

u + -17 = 13.674794331 Simplifying u + -17 = 13.674794331 Reorder the terms: -17 + u = 13.674794331 Solving -17 + u = 13.674794331 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + u = 13.674794331 + 17 Combine like terms: -17 + 17 = 0 0 + u = 13.674794331 + 17 u = 13.674794331 + 17 Combine like terms: 13.674794331 + 17 = 30.674794331 u = 30.674794331 Simplifying u = 30.674794331

Subproblem 2

u + -17 = -13.674794331 Simplifying u + -17 = -13.674794331 Reorder the terms: -17 + u = -13.674794331 Solving -17 + u = -13.674794331 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + u = -13.674794331 + 17 Combine like terms: -17 + 17 = 0 0 + u = -13.674794331 + 17 u = -13.674794331 + 17 Combine like terms: -13.674794331 + 17 = 3.325205669 u = 3.325205669 Simplifying u = 3.325205669

Solution

The solution to the problem is based on the solutions from the subproblems. u = {30.674794331, 3.325205669}

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