=x^2-37x+200

Solution for =x^2-37x+200 equation:

Simplifying
0 = x2 + -37x + 200

Reorder the terms:
0 = 200 + -37x + x2

Solving
0 = 200 + -37x + x2

Solving for variable 'x'.

Combine like terms: 0 + -200 = -200
-200 + 37x + -1x2 = 200 + -37x + x2 + -200 + 37x + -1x2

Reorder the terms:
-200 + 37x + -1x2 = 200 + -200 + -37x + 37x + x2 + -1x2

Combine like terms: 200 + -200 = 0
-200 + 37x + -1x2 = 0 + -37x + 37x + x2 + -1x2
-200 + 37x + -1x2 = -37x + 37x + x2 + -1x2

Combine like terms: -37x + 37x = 0
-200 + 37x + -1x2 = 0 + x2 + -1x2
-200 + 37x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-200 + 37x + -1x2 = 0

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

Divide each side by '-1'.
200 + -37x + x2 = 0

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -37x + -200 + x2 = 0 + -200

Reorder the terms:
200 + -200 + -37x + x2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -37x + x2 = 0 + -200
-37x + x2 = 0 + -200

Combine like terms: 0 + -200 = -200
-37x + x2 = -200

The x term is -37x.  Take half its coefficient (-18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
-37x + 342.25 + x2 = -200 + 342.25

Reorder the terms:
342.25 + -37x + x2 = -200 + 342.25

Combine like terms: -200 + 342.25 = 142.25
342.25 + -37x + x2 = 142.25

Factor a perfect square on the left side:
(x + -18.5)(x + -18.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(x + -18.5) equal to 11.926860442 and -11.926860442.

Subproblem 1
x + -18.5 = 11.926860442

Simplifying
x + -18.5 = 11.926860442

Reorder the terms:
-18.5 + x = 11.926860442

Solving
-18.5 + x = 11.926860442

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = 11.926860442 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = 11.926860442 + 18.5
x = 11.926860442 + 18.5

Combine like terms: 11.926860442 + 18.5 = 30.426860442
x = 30.426860442

Simplifying
x = 30.426860442

Subproblem 2
x + -18.5 = -11.926860442

Simplifying
x + -18.5 = -11.926860442

Reorder the terms:
-18.5 + x = -11.926860442

Solving
-18.5 + x = -11.926860442

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = -11.926860442 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = -11.926860442 + 18.5
x = -11.926860442 + 18.5

Combine like terms: -11.926860442 + 18.5 = 6.573139558
x = 6.573139558

Simplifying
x = 6.573139558

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.426860442, 6.573139558}