u^2+30u+25=0

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Solution for u^2+30u+25=0 equation: 


Simplifying
u2 + 30u + 25 = 0

Reorder the terms:
25 + 30u + u2 = 0

Solving
25 + 30u + 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 + 30u + -25 + u2 = 0 + -25

Reorder the terms:
25 + -25 + 30u + u2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 30u + u2 = 0 + -25
30u + u2 = 0 + -25

Combine like terms: 0 + -25 = -25
30u + u2 = -25

The u term is 30u.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30u + 225 + u2 = -25 + 225

Reorder the terms:
225 + 30u + u2 = -25 + 225

Combine like terms: -25 + 225 = 200
225 + 30u + u2 = 200

Factor a perfect square on the left side:
(u + 15)(u + 15) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(u + 15) equal to 14.142135624 and -14.142135624.


Subproblem 1
u + 15 = 14.142135624

Simplifying
u + 15 = 14.142135624

Reorder the terms:
15 + u = 14.142135624

Solving
15 + u = 14.142135624

Solving for variable 'u'.

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

Add '-15' to each side of the equation.
15 + -15 + u = 14.142135624 + -15

Combine like terms: 15 + -15 = 0
0 + u = 14.142135624 + -15
u = 14.142135624 + -15

Combine like terms: 14.142135624 + -15 = -0.857864376
u = -0.857864376

Simplifying
u = -0.857864376


Subproblem 2
u + 15 = -14.142135624

Simplifying
u + 15 = -14.142135624

Reorder the terms:
15 + u = -14.142135624

Solving
15 + u = -14.142135624

Solving for variable 'u'.

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

Add '-15' to each side of the equation.
15 + -15 + u = -14.142135624 + -15

Combine like terms: 15 + -15 = 0
0 + u = -14.142135624 + -15
u = -14.142135624 + -15

Combine like terms: -14.142135624 + -15 = -29.142135624
u = -29.142135624

Simplifying
u = -29.142135624


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.857864376, -29.142135624}

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