2u^2+16u+30=u^2+9

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Solution for 2u^2+16u+30=u^2+9 equation: 


Simplifying
2u2 + 16u + 30 = u2 + 9

Reorder the terms:
30 + 16u + 2u2 = u2 + 9

Reorder the terms:
30 + 16u + 2u2 = 9 + u2

Solving
30 + 16u + 2u2 = 9 + u2

Solving for variable 'u'.

Reorder the terms:
30 + -9 + 16u + 2u2 + -1u2 = 9 + u2 + -9 + -1u2

Combine like terms: 30 + -9 = 21
21 + 16u + 2u2 + -1u2 = 9 + u2 + -9 + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
21 + 16u + 1u2 = 9 + u2 + -9 + -1u2

Reorder the terms:
21 + 16u + 1u2 = 9 + -9 + u2 + -1u2

Combine like terms: 9 + -9 = 0
21 + 16u + 1u2 = 0 + u2 + -1u2
21 + 16u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
21 + 16u + 1u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 16u + -21 + u2 = 0 + -21

Reorder the terms:
21 + -21 + 16u + u2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 16u + u2 = 0 + -21
16u + u2 = 0 + -21

Combine like terms: 0 + -21 = -21
16u + u2 = -21

The u term is 16u.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16u + 64 + u2 = -21 + 64

Reorder the terms:
64 + 16u + u2 = -21 + 64

Combine like terms: -21 + 64 = 43
64 + 16u + u2 = 43

Factor a perfect square on the left side:
(u + 8)(u + 8) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(u + 8) equal to 6.557438524 and -6.557438524.


Subproblem 1
u + 8 = 6.557438524

Simplifying
u + 8 = 6.557438524

Reorder the terms:
8 + u = 6.557438524

Solving
8 + u = 6.557438524

Solving for variable 'u'.

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

Add '-8' to each side of the equation.
8 + -8 + u = 6.557438524 + -8

Combine like terms: 8 + -8 = 0
0 + u = 6.557438524 + -8
u = 6.557438524 + -8

Combine like terms: 6.557438524 + -8 = -1.442561476
u = -1.442561476

Simplifying
u = -1.442561476


Subproblem 2
u + 8 = -6.557438524

Simplifying
u + 8 = -6.557438524

Reorder the terms:
8 + u = -6.557438524

Solving
8 + u = -6.557438524

Solving for variable 'u'.

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

Add '-8' to each side of the equation.
8 + -8 + u = -6.557438524 + -8

Combine like terms: 8 + -8 = 0
0 + u = -6.557438524 + -8
u = -6.557438524 + -8

Combine like terms: -6.557438524 + -8 = -14.557438524
u = -14.557438524

Simplifying
u = -14.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-1.442561476, -14.557438524}

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