0=x^2+150x-5000

Solution for 0=x^2+150x-5000 equation:

Simplifying
0 = x2 + 150x + -5000

Reorder the terms:
0 = -5000 + 150x + x2

Solving
0 = -5000 + 150x + x2

Solving for variable 'x'.

Combine like terms: 0 + 5000 = 5000
5000 + -150x + -1x2 = -5000 + 150x + x2 + 5000 + -150x + -1x2

Reorder the terms:
5000 + -150x + -1x2 = -5000 + 5000 + 150x + -150x + x2 + -1x2

Combine like terms: -5000 + 5000 = 0
5000 + -150x + -1x2 = 0 + 150x + -150x + x2 + -1x2
5000 + -150x + -1x2 = 150x + -150x + x2 + -1x2

Combine like terms: 150x + -150x = 0
5000 + -150x + -1x2 = 0 + x2 + -1x2
5000 + -150x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5000 + -150x + -1x2 = 0

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

Divide each side by '-1'.
-5000 + 150x + x2 = 0

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + 150x + 5000 + x2 = 0 + 5000

Reorder the terms:
-5000 + 5000 + 150x + x2 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + 150x + x2 = 0 + 5000
150x + x2 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
150x + x2 = 5000

The x term is 150x.  Take half its coefficient (75).
Square it (5625) and add it to both sides.

Add '5625' to each side of the equation.
150x + 5625 + x2 = 5000 + 5625

Reorder the terms:
5625 + 150x + x2 = 5000 + 5625

Combine like terms: 5000 + 5625 = 10625
5625 + 150x + x2 = 10625

Factor a perfect square on the left side:
(x + 75)(x + 75) = 10625

Calculate the square root of the right side: 103.07764064

Break this problem into two subproblems by setting 
(x + 75) equal to 103.07764064 and -103.07764064.

Subproblem 1
x + 75 = 103.07764064

Simplifying
x + 75 = 103.07764064

Reorder the terms:
75 + x = 103.07764064

Solving
75 + x = 103.07764064

Solving for variable 'x'.

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

Add '-75' to each side of the equation.
75 + -75 + x = 103.07764064 + -75

Combine like terms: 75 + -75 = 0
0 + x = 103.07764064 + -75
x = 103.07764064 + -75

Combine like terms: 103.07764064 + -75 = 28.07764064
x = 28.07764064

Simplifying
x = 28.07764064

Subproblem 2
x + 75 = -103.07764064

Simplifying
x + 75 = -103.07764064

Reorder the terms:
75 + x = -103.07764064

Solving
75 + x = -103.07764064

Solving for variable 'x'.

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

Add '-75' to each side of the equation.
75 + -75 + x = -103.07764064 + -75

Combine like terms: 75 + -75 = 0
0 + x = -103.07764064 + -75
x = -103.07764064 + -75

Combine like terms: -103.07764064 + -75 = -178.07764064
x = -178.07764064

Simplifying
x = -178.07764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.07764064, -178.07764064}