u^2-97u-1296=0

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Solution for u^2-97u-1296=0 equation: 


Simplifying
u2 + -97u + -1296 = 0

Reorder the terms:
-1296 + -97u + u2 = 0

Solving
-1296 + -97u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '1296' to each side of the equation.
-1296 + -97u + 1296 + u2 = 0 + 1296

Reorder the terms:
-1296 + 1296 + -97u + u2 = 0 + 1296

Combine like terms: -1296 + 1296 = 0
0 + -97u + u2 = 0 + 1296
-97u + u2 = 0 + 1296

Combine like terms: 0 + 1296 = 1296
-97u + u2 = 1296

The u term is -97u.  Take half its coefficient (-48.5).
Square it (2352.25) and add it to both sides.

Add '2352.25' to each side of the equation.
-97u + 2352.25 + u2 = 1296 + 2352.25

Reorder the terms:
2352.25 + -97u + u2 = 1296 + 2352.25

Combine like terms: 1296 + 2352.25 = 3648.25
2352.25 + -97u + u2 = 3648.25

Factor a perfect square on the left side:
(u + -48.5)(u + -48.5) = 3648.25

Calculate the square root of the right side: 60.400745029

Break this problem into two subproblems by setting 
(u + -48.5) equal to 60.400745029 and -60.400745029.


Subproblem 1
u + -48.5 = 60.400745029

Simplifying
u + -48.5 = 60.400745029

Reorder the terms:
-48.5 + u = 60.400745029

Solving
-48.5 + u = 60.400745029

Solving for variable 'u'.

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

Add '48.5' to each side of the equation.
-48.5 + 48.5 + u = 60.400745029 + 48.5

Combine like terms: -48.5 + 48.5 = 0.0
0.0 + u = 60.400745029 + 48.5
u = 60.400745029 + 48.5

Combine like terms: 60.400745029 + 48.5 = 108.900745029
u = 108.900745029

Simplifying
u = 108.900745029


Subproblem 2
u + -48.5 = -60.400745029

Simplifying
u + -48.5 = -60.400745029

Reorder the terms:
-48.5 + u = -60.400745029

Solving
-48.5 + u = -60.400745029

Solving for variable 'u'.

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

Add '48.5' to each side of the equation.
-48.5 + 48.5 + u = -60.400745029 + 48.5

Combine like terms: -48.5 + 48.5 = 0.0
0.0 + u = -60.400745029 + 48.5
u = -60.400745029 + 48.5

Combine like terms: -60.400745029 + 48.5 = -11.900745029
u = -11.900745029

Simplifying
u = -11.900745029


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {108.900745029, -11.900745029}

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