u^2+2u-9=0

Solution for u^2+2u-9=0 equation:

Simplifying
u2 + 2u + -9 = 0

Reorder the terms:
-9 + 2u + u2 = 0

Solving
-9 + 2u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2u + 9 + u2 = 0 + 9

Reorder the terms:
-9 + 9 + 2u + u2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2u + u2 = 0 + 9
2u + u2 = 0 + 9

Combine like terms: 0 + 9 = 9
2u + u2 = 9

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 = 9 + 1

Reorder the terms:
1 + 2u + u2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + 2u + u2 = 10

Factor a perfect square on the left side:
(u + 1)(u + 1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(u + 1) equal to 3.16227766 and -3.16227766.

Subproblem 1
u + 1 = 3.16227766

Simplifying
u + 1 = 3.16227766

Reorder the terms:
1 + u = 3.16227766

Solving
1 + u = 3.16227766

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 = 3.16227766 + -1

Combine like terms: 1 + -1 = 0
0 + u = 3.16227766 + -1
u = 3.16227766 + -1

Combine like terms: 3.16227766 + -1 = 2.16227766
u = 2.16227766

Simplifying
u = 2.16227766

Subproblem 2
u + 1 = -3.16227766

Simplifying
u + 1 = -3.16227766

Reorder the terms:
1 + u = -3.16227766

Solving
1 + u = -3.16227766

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 = -3.16227766 + -1

Combine like terms: 1 + -1 = 0
0 + u = -3.16227766 + -1
u = -3.16227766 + -1

Combine like terms: -3.16227766 + -1 = -4.16227766
u = -4.16227766

Simplifying
u = -4.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.16227766, -4.16227766}