u-5*u-5=2u^2-14u+4

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Solution for u-5*u-5=2u^2-14u+4 equation: 


Simplifying
u + -5u + -5 = 2u2 + -14u + 4

Reorder the terms:
-5 + u + -5u = 2u2 + -14u + 4

Combine like terms: u + -5u = -4u
-5 + -4u = 2u2 + -14u + 4

Reorder the terms:
-5 + -4u = 4 + -14u + 2u2

Solving
-5 + -4u = 4 + -14u + 2u2

Solving for variable 'u'.

Reorder the terms:
-5 + -4 + -4u + 14u + -2u2 = 4 + -14u + 2u2 + -4 + 14u + -2u2

Combine like terms: -5 + -4 = -9
-9 + -4u + 14u + -2u2 = 4 + -14u + 2u2 + -4 + 14u + -2u2

Combine like terms: -4u + 14u = 10u
-9 + 10u + -2u2 = 4 + -14u + 2u2 + -4 + 14u + -2u2

Reorder the terms:
-9 + 10u + -2u2 = 4 + -4 + -14u + 14u + 2u2 + -2u2

Combine like terms: 4 + -4 = 0
-9 + 10u + -2u2 = 0 + -14u + 14u + 2u2 + -2u2
-9 + 10u + -2u2 = -14u + 14u + 2u2 + -2u2

Combine like terms: -14u + 14u = 0
-9 + 10u + -2u2 = 0 + 2u2 + -2u2
-9 + 10u + -2u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-9 + 10u + -2u2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
4.5 + -5u + u2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -5u + -4.5 + u2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -5u + u2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -5u + u2 = 0 + -4.5
-5u + u2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-5u + u2 = -4.5

The u term is -5u.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5u + 6.25 + u2 = -4.5 + 6.25

Reorder the terms:
6.25 + -5u + u2 = -4.5 + 6.25

Combine like terms: -4.5 + 6.25 = 1.75
6.25 + -5u + u2 = 1.75

Factor a perfect square on the left side:
(u + -2.5)(u + -2.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(u + -2.5) equal to 1.322875656 and -1.322875656.


Subproblem 1
u + -2.5 = 1.322875656

Simplifying
u + -2.5 = 1.322875656

Reorder the terms:
-2.5 + u = 1.322875656

Solving
-2.5 + u = 1.322875656

Solving for variable 'u'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + u = 1.322875656 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = 1.322875656 + 2.5
u = 1.322875656 + 2.5

Combine like terms: 1.322875656 + 2.5 = 3.822875656
u = 3.822875656

Simplifying
u = 3.822875656


Subproblem 2
u + -2.5 = -1.322875656

Simplifying
u + -2.5 = -1.322875656

Reorder the terms:
-2.5 + u = -1.322875656

Solving
-2.5 + u = -1.322875656

Solving for variable 'u'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + u = -1.322875656 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = -1.322875656 + 2.5
u = -1.322875656 + 2.5

Combine like terms: -1.322875656 + 2.5 = 1.177124344
u = 1.177124344

Simplifying
u = 1.177124344


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.822875656, 1.177124344}

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