u^2+49=2u^2+21u+61

Solution for u^2+49=2u^2+21u+61 equation:

Simplifying
u2 + 49 = 2u2 + 21u + 61

Reorder the terms:
49 + u2 = 2u2 + 21u + 61

Reorder the terms:
49 + u2 = 61 + 21u + 2u2

Solving
49 + u2 = 61 + 21u + 2u2

Solving for variable 'u'.

Reorder the terms:
49 + -61 + -21u + u2 + -2u2 = 61 + 21u + 2u2 + -61 + -21u + -2u2

Combine like terms: 49 + -61 = -12
-12 + -21u + u2 + -2u2 = 61 + 21u + 2u2 + -61 + -21u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-12 + -21u + -1u2 = 61 + 21u + 2u2 + -61 + -21u + -2u2

Reorder the terms:
-12 + -21u + -1u2 = 61 + -61 + 21u + -21u + 2u2 + -2u2

Combine like terms: 61 + -61 = 0
-12 + -21u + -1u2 = 0 + 21u + -21u + 2u2 + -2u2
-12 + -21u + -1u2 = 21u + -21u + 2u2 + -2u2

Combine like terms: 21u + -21u = 0
-12 + -21u + -1u2 = 0 + 2u2 + -2u2
-12 + -21u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-12 + -21u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 21u + u2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(12 + 21u + u2)' equal to zero and attempt to solve:

Simplifying
12 + 21u + u2 = 0

Solving
12 + 21u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 21u + -12 + u2 = 0 + -12

Reorder the terms:
12 + -12 + 21u + u2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 21u + u2 = 0 + -12
21u + u2 = 0 + -12

Combine like terms: 0 + -12 = -12
21u + u2 = -12

The u term is 21u.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21u + 110.25 + u2 = -12 + 110.25

Reorder the terms:
110.25 + 21u + u2 = -12 + 110.25

Combine like terms: -12 + 110.25 = 98.25
110.25 + 21u + u2 = 98.25

Factor a perfect square on the left side:
(u + 10.5)(u + 10.5) = 98.25

Calculate the square root of the right side: 9.912113801

Break this problem into two subproblems by setting 
(u + 10.5) equal to 9.912113801 and -9.912113801.

Subproblem 1
u + 10.5 = 9.912113801

Simplifying
u + 10.5 = 9.912113801

Reorder the terms:
10.5 + u = 9.912113801

Solving
10.5 + u = 9.912113801

Solving for variable 'u'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + u = 9.912113801 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + u = 9.912113801 + -10.5
u = 9.912113801 + -10.5

Combine like terms: 9.912113801 + -10.5 = -0.587886199
u = -0.587886199

Simplifying
u = -0.587886199

Subproblem 2
u + 10.5 = -9.912113801

Simplifying
u + 10.5 = -9.912113801

Reorder the terms:
10.5 + u = -9.912113801

Solving
10.5 + u = -9.912113801

Solving for variable 'u'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + u = -9.912113801 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + u = -9.912113801 + -10.5
u = -9.912113801 + -10.5

Combine like terms: -9.912113801 + -10.5 = -20.412113801
u = -20.412113801

Simplifying
u = -20.412113801

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.587886199, -20.412113801}
Solution
u = {-0.587886199, -20.412113801}