x^2-36x-275=0

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Solution for x^2-36x-275=0 equation: 


Simplifying
x2 + -36x + -275 = 0

Reorder the terms:
-275 + -36x + x2 = 0

Solving
-275 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '275' to each side of the equation.
-275 + -36x + 275 + x2 = 0 + 275

Reorder the terms:
-275 + 275 + -36x + x2 = 0 + 275

Combine like terms: -275 + 275 = 0
0 + -36x + x2 = 0 + 275
-36x + x2 = 0 + 275

Combine like terms: 0 + 275 = 275
-36x + x2 = 275

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 = 275 + 324

Reorder the terms:
324 + -36x + x2 = 275 + 324

Combine like terms: 275 + 324 = 599
324 + -36x + x2 = 599

Factor a perfect square on the left side:
(x + -18)(x + -18) = 599

Calculate the square root of the right side: 24.474476501

Break this problem into two subproblems by setting 
(x + -18) equal to 24.474476501 and -24.474476501.


Subproblem 1
x + -18 = 24.474476501

Simplifying
x + -18 = 24.474476501

Reorder the terms:
-18 + x = 24.474476501

Solving
-18 + x = 24.474476501

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 = 24.474476501 + 18

Combine like terms: -18 + 18 = 0
0 + x = 24.474476501 + 18
x = 24.474476501 + 18

Combine like terms: 24.474476501 + 18 = 42.474476501
x = 42.474476501

Simplifying
x = 42.474476501


Subproblem 2
x + -18 = -24.474476501

Simplifying
x + -18 = -24.474476501

Reorder the terms:
-18 + x = -24.474476501

Solving
-18 + x = -24.474476501

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 = -24.474476501 + 18

Combine like terms: -18 + 18 = 0
0 + x = -24.474476501 + 18
x = -24.474476501 + 18

Combine like terms: -24.474476501 + 18 = -6.474476501
x = -6.474476501

Simplifying
x = -6.474476501


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.474476501, -6.474476501}

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