u^2-2u-49=0

Solution for u^2-2u-49=0 equation:

Simplifying
u2 + -2u + -49 = 0

Reorder the terms:
-49 + -2u + u2 = 0

Solving
-49 + -2u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -2u + 49 + u2 = 0 + 49

Reorder the terms:
-49 + 49 + -2u + u2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -2u + u2 = 0 + 49
-2u + u2 = 0 + 49

Combine like terms: 0 + 49 = 49
-2u + u2 = 49

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 = 49 + 1

Reorder the terms:
1 + -2u + u2 = 49 + 1

Combine like terms: 49 + 1 = 50
1 + -2u + u2 = 50

Factor a perfect square on the left side:
(u + -1)(u + -1) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(u + -1) equal to 7.071067812 and -7.071067812.

Subproblem 1
u + -1 = 7.071067812

Simplifying
u + -1 = 7.071067812

Reorder the terms:
-1 + u = 7.071067812

Solving
-1 + u = 7.071067812

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 = 7.071067812 + 1

Combine like terms: -1 + 1 = 0
0 + u = 7.071067812 + 1
u = 7.071067812 + 1

Combine like terms: 7.071067812 + 1 = 8.071067812
u = 8.071067812

Simplifying
u = 8.071067812

Subproblem 2
u + -1 = -7.071067812

Simplifying
u + -1 = -7.071067812

Reorder the terms:
-1 + u = -7.071067812

Solving
-1 + u = -7.071067812

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 = -7.071067812 + 1

Combine like terms: -1 + 1 = 0
0 + u = -7.071067812 + 1
u = -7.071067812 + 1

Combine like terms: -7.071067812 + 1 = -6.071067812
u = -6.071067812

Simplifying
u = -6.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {8.071067812, -6.071067812}