(u^2)-2u-21=0

Solution for (u^2)-2u-21=0 equation:

Simplifying
(u2) + -2u + -21 = 0
u2 + -2u + -21 = 0

Reorder the terms:
-21 + -2u + u2 = 0

Solving
-21 + -2u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -2u + 21 + u2 = 0 + 21

Reorder the terms:
-21 + 21 + -2u + u2 = 0 + 21

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

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

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 = 21 + 1

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

Combine like terms: 21 + 1 = 22
1 + -2u + u2 = 22

Factor a perfect square on the left side:
(u + -1)(u + -1) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(u + -1) equal to 4.69041576 and -4.69041576.

Subproblem 1
u + -1 = 4.69041576

Simplifying
u + -1 = 4.69041576

Reorder the terms:
-1 + u = 4.69041576

Solving
-1 + u = 4.69041576

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 = 4.69041576 + 1

Combine like terms: -1 + 1 = 0
0 + u = 4.69041576 + 1
u = 4.69041576 + 1

Combine like terms: 4.69041576 + 1 = 5.69041576
u = 5.69041576

Simplifying
u = 5.69041576

Subproblem 2
u + -1 = -4.69041576

Simplifying
u + -1 = -4.69041576

Reorder the terms:
-1 + u = -4.69041576

Solving
-1 + u = -4.69041576

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 = -4.69041576 + 1

Combine like terms: -1 + 1 = 0
0 + u = -4.69041576 + 1
u = -4.69041576 + 1

Combine like terms: -4.69041576 + 1 = -3.69041576
u = -3.69041576

Simplifying
u = -3.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.69041576, -3.69041576}