x^2-36x-13=0

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Solution for x^2-36x-13=0 equation: 


Simplifying
x2 + -36x + -13 = 0

Reorder the terms:
-13 + -36x + x2 = 0

Solving
-13 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -36x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -36x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -36x + x2 = 0 + 13
-36x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-36x + x2 = 13

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 = 13 + 324

Reorder the terms:
324 + -36x + x2 = 13 + 324

Combine like terms: 13 + 324 = 337
324 + -36x + x2 = 337

Factor a perfect square on the left side:
(x + -18)(x + -18) = 337

Calculate the square root of the right side: 18.357559751

Break this problem into two subproblems by setting 
(x + -18) equal to 18.357559751 and -18.357559751.


Subproblem 1
x + -18 = 18.357559751

Simplifying
x + -18 = 18.357559751

Reorder the terms:
-18 + x = 18.357559751

Solving
-18 + x = 18.357559751

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 = 18.357559751 + 18

Combine like terms: -18 + 18 = 0
0 + x = 18.357559751 + 18
x = 18.357559751 + 18

Combine like terms: 18.357559751 + 18 = 36.357559751
x = 36.357559751

Simplifying
x = 36.357559751


Subproblem 2
x + -18 = -18.357559751

Simplifying
x + -18 = -18.357559751

Reorder the terms:
-18 + x = -18.357559751

Solving
-18 + x = -18.357559751

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 = -18.357559751 + 18

Combine like terms: -18 + 18 = 0
0 + x = -18.357559751 + 18
x = -18.357559751 + 18

Combine like terms: -18.357559751 + 18 = -0.357559751
x = -0.357559751

Simplifying
x = -0.357559751


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.357559751, -0.357559751}

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