u^2+2u-29=0

Solution for u^2+2u-29=0 equation:

Simplifying
u2 + 2u + -29 = 0

Reorder the terms:
-29 + 2u + u2 = 0

Solving
-29 + 2u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 2u + 29 + u2 = 0 + 29

Reorder the terms:
-29 + 29 + 2u + u2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 2u + u2 = 0 + 29
2u + u2 = 0 + 29

Combine like terms: 0 + 29 = 29
2u + u2 = 29

The u term is 2u.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2u + 1 + u2 = 29 + 1

Reorder the terms:
1 + 2u + u2 = 29 + 1

Combine like terms: 29 + 1 = 30
1 + 2u + u2 = 30

Factor a perfect square on the left side:
(u + 1)(u + 1) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(u + 1) equal to 5.477225575 and -5.477225575.

Subproblem 1
u + 1 = 5.477225575

Simplifying
u + 1 = 5.477225575

Reorder the terms:
1 + u = 5.477225575

Solving
1 + u = 5.477225575

Solving for variable 'u'.

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

Add '-1' to each side of the equation.
1 + -1 + u = 5.477225575 + -1

Combine like terms: 1 + -1 = 0
0 + u = 5.477225575 + -1
u = 5.477225575 + -1

Combine like terms: 5.477225575 + -1 = 4.477225575
u = 4.477225575

Simplifying
u = 4.477225575

Subproblem 2
u + 1 = -5.477225575

Simplifying
u + 1 = -5.477225575

Reorder the terms:
1 + u = -5.477225575

Solving
1 + u = -5.477225575

Solving for variable 'u'.

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

Add '-1' to each side of the equation.
1 + -1 + u = -5.477225575 + -1

Combine like terms: 1 + -1 = 0
0 + u = -5.477225575 + -1
u = -5.477225575 + -1

Combine like terms: -5.477225575 + -1 = -6.477225575
u = -6.477225575

Simplifying
u = -6.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {4.477225575, -6.477225575}