x^2-36x+19=0

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Solution for x^2-36x+19=0 equation: 


Simplifying
x2 + -36x + 19 = 0

Reorder the terms:
19 + -36x + x2 = 0

Solving
19 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -36x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + -36x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -36x + x2 = 0 + -19
-36x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
-36x + x2 = -19

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = -19 + 324

Reorder the terms:
324 + -36x + x2 = -19 + 324

Combine like terms: -19 + 324 = 305
324 + -36x + x2 = 305

Factor a perfect square on the left side:
(x + -18)(x + -18) = 305

Calculate the square root of the right side: 17.464249197

Break this problem into two subproblems by setting 
(x + -18) equal to 17.464249197 and -17.464249197.


Subproblem 1
x + -18 = 17.464249197

Simplifying
x + -18 = 17.464249197

Reorder the terms:
-18 + x = 17.464249197

Solving
-18 + x = 17.464249197

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = 17.464249197 + 18

Combine like terms: -18 + 18 = 0
0 + x = 17.464249197 + 18
x = 17.464249197 + 18

Combine like terms: 17.464249197 + 18 = 35.464249197
x = 35.464249197

Simplifying
x = 35.464249197


Subproblem 2
x + -18 = -17.464249197

Simplifying
x + -18 = -17.464249197

Reorder the terms:
-18 + x = -17.464249197

Solving
-18 + x = -17.464249197

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = -17.464249197 + 18

Combine like terms: -18 + 18 = 0
0 + x = -17.464249197 + 18
x = -17.464249197 + 18

Combine like terms: -17.464249197 + 18 = 0.535750803
x = 0.535750803

Simplifying
x = 0.535750803


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.464249197, 0.535750803}

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