u^2+22u+25=0

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Solution for u^2+22u+25=0 equation: 


Simplifying
u2 + 22u + 25 = 0

Reorder the terms:
25 + 22u + u2 = 0

Solving
25 + 22u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 22u + -25 + u2 = 0 + -25

Reorder the terms:
25 + -25 + 22u + u2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 22u + u2 = 0 + -25
22u + u2 = 0 + -25

Combine like terms: 0 + -25 = -25
22u + u2 = -25

The u term is 22u.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22u + 121 + u2 = -25 + 121

Reorder the terms:
121 + 22u + u2 = -25 + 121

Combine like terms: -25 + 121 = 96
121 + 22u + u2 = 96

Factor a perfect square on the left side:
(u + 11)(u + 11) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(u + 11) equal to 9.797958971 and -9.797958971.


Subproblem 1
u + 11 = 9.797958971

Simplifying
u + 11 = 9.797958971

Reorder the terms:
11 + u = 9.797958971

Solving
11 + u = 9.797958971

Solving for variable 'u'.

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

Add '-11' to each side of the equation.
11 + -11 + u = 9.797958971 + -11

Combine like terms: 11 + -11 = 0
0 + u = 9.797958971 + -11
u = 9.797958971 + -11

Combine like terms: 9.797958971 + -11 = -1.202041029
u = -1.202041029

Simplifying
u = -1.202041029


Subproblem 2
u + 11 = -9.797958971

Simplifying
u + 11 = -9.797958971

Reorder the terms:
11 + u = -9.797958971

Solving
11 + u = -9.797958971

Solving for variable 'u'.

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

Add '-11' to each side of the equation.
11 + -11 + u = -9.797958971 + -11

Combine like terms: 11 + -11 = 0
0 + u = -9.797958971 + -11
u = -9.797958971 + -11

Combine like terms: -9.797958971 + -11 = -20.797958971
u = -20.797958971

Simplifying
u = -20.797958971


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-1.202041029, -20.797958971}

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