0=x^2+50x-1140

Solution for 0=x^2+50x-1140 equation:

Simplifying
0 = x2 + 50x + -1140

Reorder the terms:
0 = -1140 + 50x + x2

Solving
0 = -1140 + 50x + x2

Solving for variable 'x'.

Combine like terms: 0 + 1140 = 1140
1140 + -50x + -1x2 = -1140 + 50x + x2 + 1140 + -50x + -1x2

Reorder the terms:
1140 + -50x + -1x2 = -1140 + 1140 + 50x + -50x + x2 + -1x2

Combine like terms: -1140 + 1140 = 0
1140 + -50x + -1x2 = 0 + 50x + -50x + x2 + -1x2
1140 + -50x + -1x2 = 50x + -50x + x2 + -1x2

Combine like terms: 50x + -50x = 0
1140 + -50x + -1x2 = 0 + x2 + -1x2
1140 + -50x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1140 + -50x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1140 + 50x + x2 = 0

Move the constant term to the right:

Add '1140' to each side of the equation.
-1140 + 50x + 1140 + x2 = 0 + 1140

Reorder the terms:
-1140 + 1140 + 50x + x2 = 0 + 1140

Combine like terms: -1140 + 1140 = 0
0 + 50x + x2 = 0 + 1140
50x + x2 = 0 + 1140

Combine like terms: 0 + 1140 = 1140
50x + x2 = 1140

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 1140 + 625

Reorder the terms:
625 + 50x + x2 = 1140 + 625

Combine like terms: 1140 + 625 = 1765
625 + 50x + x2 = 1765

Factor a perfect square on the left side:
(x + 25)(x + 25) = 1765

Calculate the square root of the right side: 42.011903075

Break this problem into two subproblems by setting 
(x + 25) equal to 42.011903075 and -42.011903075.

Subproblem 1
x + 25 = 42.011903075

Simplifying
x + 25 = 42.011903075

Reorder the terms:
25 + x = 42.011903075

Solving
25 + x = 42.011903075

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 42.011903075 + -25

Combine like terms: 25 + -25 = 0
0 + x = 42.011903075 + -25
x = 42.011903075 + -25

Combine like terms: 42.011903075 + -25 = 17.011903075
x = 17.011903075

Simplifying
x = 17.011903075

Subproblem 2
x + 25 = -42.011903075

Simplifying
x + 25 = -42.011903075

Reorder the terms:
25 + x = -42.011903075

Solving
25 + x = -42.011903075

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -42.011903075 + -25

Combine like terms: 25 + -25 = 0
0 + x = -42.011903075 + -25
x = -42.011903075 + -25

Combine like terms: -42.011903075 + -25 = -67.011903075
x = -67.011903075

Simplifying
x = -67.011903075

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.011903075, -67.011903075}