u^2-67u+636.5=0

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Solution for u^2-67u+636.5=0 equation: 


Simplifying
u2 + -67u + 636.5 = 0

Reorder the terms:
636.5 + -67u + u2 = 0

Solving
636.5 + -67u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-636.5' to each side of the equation.
636.5 + -67u + -636.5 + u2 = 0 + -636.5

Reorder the terms:
636.5 + -636.5 + -67u + u2 = 0 + -636.5

Combine like terms: 636.5 + -636.5 = 0.0
0.0 + -67u + u2 = 0 + -636.5
-67u + u2 = 0 + -636.5

Combine like terms: 0 + -636.5 = -636.5
-67u + u2 = -636.5

The u term is -67u.  Take half its coefficient (-33.5).
Square it (1122.25) and add it to both sides.

Add '1122.25' to each side of the equation.
-67u + 1122.25 + u2 = -636.5 + 1122.25

Reorder the terms:
1122.25 + -67u + u2 = -636.5 + 1122.25

Combine like terms: -636.5 + 1122.25 = 485.75
1122.25 + -67u + u2 = 485.75

Factor a perfect square on the left side:
(u + -33.5)(u + -33.5) = 485.75

Calculate the square root of the right side: 22.039736841

Break this problem into two subproblems by setting 
(u + -33.5) equal to 22.039736841 and -22.039736841.


Subproblem 1
u + -33.5 = 22.039736841

Simplifying
u + -33.5 = 22.039736841

Reorder the terms:
-33.5 + u = 22.039736841

Solving
-33.5 + u = 22.039736841

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '33.5' to each side of the equation.
-33.5 + 33.5 + u = 22.039736841 + 33.5

Combine like terms: -33.5 + 33.5 = 0.0
0.0 + u = 22.039736841 + 33.5
u = 22.039736841 + 33.5

Combine like terms: 22.039736841 + 33.5 = 55.539736841
u = 55.539736841

Simplifying
u = 55.539736841


Subproblem 2
u + -33.5 = -22.039736841

Simplifying
u + -33.5 = -22.039736841

Reorder the terms:
-33.5 + u = -22.039736841

Solving
-33.5 + u = -22.039736841

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '33.5' to each side of the equation.
-33.5 + 33.5 + u = -22.039736841 + 33.5

Combine like terms: -33.5 + 33.5 = 0.0
0.0 + u = -22.039736841 + 33.5
u = -22.039736841 + 33.5

Combine like terms: -22.039736841 + 33.5 = 11.460263159
u = 11.460263159

Simplifying
u = 11.460263159


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {55.539736841, 11.460263159}

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