x^2-36x-550=0

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Solution for x^2-36x-550=0 equation: 


Simplifying
x2 + -36x + -550 = 0

Reorder the terms:
-550 + -36x + x2 = 0

Solving
-550 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '550' to each side of the equation.
-550 + -36x + 550 + x2 = 0 + 550

Reorder the terms:
-550 + 550 + -36x + x2 = 0 + 550

Combine like terms: -550 + 550 = 0
0 + -36x + x2 = 0 + 550
-36x + x2 = 0 + 550

Combine like terms: 0 + 550 = 550
-36x + x2 = 550

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 = 550 + 324

Reorder the terms:
324 + -36x + x2 = 550 + 324

Combine like terms: 550 + 324 = 874
324 + -36x + x2 = 874

Factor a perfect square on the left side:
(x + -18)(x + -18) = 874

Calculate the square root of the right side: 29.563490998

Break this problem into two subproblems by setting 
(x + -18) equal to 29.563490998 and -29.563490998.


Subproblem 1
x + -18 = 29.563490998

Simplifying
x + -18 = 29.563490998

Reorder the terms:
-18 + x = 29.563490998

Solving
-18 + x = 29.563490998

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 = 29.563490998 + 18

Combine like terms: -18 + 18 = 0
0 + x = 29.563490998 + 18
x = 29.563490998 + 18

Combine like terms: 29.563490998 + 18 = 47.563490998
x = 47.563490998

Simplifying
x = 47.563490998


Subproblem 2
x + -18 = -29.563490998

Simplifying
x + -18 = -29.563490998

Reorder the terms:
-18 + x = -29.563490998

Solving
-18 + x = -29.563490998

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 = -29.563490998 + 18

Combine like terms: -18 + 18 = 0
0 + x = -29.563490998 + 18
x = -29.563490998 + 18

Combine like terms: -29.563490998 + 18 = -11.563490998
x = -11.563490998

Simplifying
x = -11.563490998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.563490998, -11.563490998}

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