2u^2+5u+13=u^2-2u+2

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Solution for 2u^2+5u+13=u^2-2u+2 equation: 


Simplifying
2u2 + 5u + 13 = u2 + -2u + 2

Reorder the terms:
13 + 5u + 2u2 = u2 + -2u + 2

Reorder the terms:
13 + 5u + 2u2 = 2 + -2u + u2

Solving
13 + 5u + 2u2 = 2 + -2u + u2

Solving for variable 'u'.

Reorder the terms:
13 + -2 + 5u + 2u + 2u2 + -1u2 = 2 + -2u + u2 + -2 + 2u + -1u2

Combine like terms: 13 + -2 = 11
11 + 5u + 2u + 2u2 + -1u2 = 2 + -2u + u2 + -2 + 2u + -1u2

Combine like terms: 5u + 2u = 7u
11 + 7u + 2u2 + -1u2 = 2 + -2u + u2 + -2 + 2u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
11 + 7u + 1u2 = 2 + -2u + u2 + -2 + 2u + -1u2

Reorder the terms:
11 + 7u + 1u2 = 2 + -2 + -2u + 2u + u2 + -1u2

Combine like terms: 2 + -2 = 0
11 + 7u + 1u2 = 0 + -2u + 2u + u2 + -1u2
11 + 7u + 1u2 = -2u + 2u + u2 + -1u2

Combine like terms: -2u + 2u = 0
11 + 7u + 1u2 = 0 + u2 + -1u2
11 + 7u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
11 + 7u + 1u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 7u + -11 + u2 = 0 + -11

Reorder the terms:
11 + -11 + 7u + u2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 7u + u2 = 0 + -11
7u + u2 = 0 + -11

Combine like terms: 0 + -11 = -11
7u + u2 = -11

The u term is 7u.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7u + 12.25 + u2 = -11 + 12.25

Reorder the terms:
12.25 + 7u + u2 = -11 + 12.25

Combine like terms: -11 + 12.25 = 1.25
12.25 + 7u + u2 = 1.25

Factor a perfect square on the left side:
(u + 3.5)(u + 3.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(u + 3.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
u + 3.5 = 1.118033989

Simplifying
u + 3.5 = 1.118033989

Reorder the terms:
3.5 + u = 1.118033989

Solving
3.5 + u = 1.118033989

Solving for variable 'u'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + u = 1.118033989 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + u = 1.118033989 + -3.5
u = 1.118033989 + -3.5

Combine like terms: 1.118033989 + -3.5 = -2.381966011
u = -2.381966011

Simplifying
u = -2.381966011


Subproblem 2
u + 3.5 = -1.118033989

Simplifying
u + 3.5 = -1.118033989

Reorder the terms:
3.5 + u = -1.118033989

Solving
3.5 + u = -1.118033989

Solving for variable 'u'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + u = -1.118033989 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + u = -1.118033989 + -3.5
u = -1.118033989 + -3.5

Combine like terms: -1.118033989 + -3.5 = -4.618033989
u = -4.618033989

Simplifying
u = -4.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-2.381966011, -4.618033989}

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