-x^2+36x-20=0

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Solution for -x^2+36x-20=0 equation: 


Simplifying
-1x2 + 36x + -20 = 0

Reorder the terms:
-20 + 36x + -1x2 = 0

Solving
-20 + 36x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
20 + -36x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -36x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -36x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -36x + x2 = 0 + -20
-36x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-36x + x2 = -20

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 = -20 + 324

Reorder the terms:
324 + -36x + x2 = -20 + 324

Combine like terms: -20 + 324 = 304
324 + -36x + x2 = 304

Factor a perfect square on the left side:
(x + -18)(x + -18) = 304

Calculate the square root of the right side: 17.435595774

Break this problem into two subproblems by setting 
(x + -18) equal to 17.435595774 and -17.435595774.


Subproblem 1
x + -18 = 17.435595774

Simplifying
x + -18 = 17.435595774

Reorder the terms:
-18 + x = 17.435595774

Solving
-18 + x = 17.435595774

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 = 17.435595774 + 18

Combine like terms: -18 + 18 = 0
0 + x = 17.435595774 + 18
x = 17.435595774 + 18

Combine like terms: 17.435595774 + 18 = 35.435595774
x = 35.435595774

Simplifying
x = 35.435595774


Subproblem 2
x + -18 = -17.435595774

Simplifying
x + -18 = -17.435595774

Reorder the terms:
-18 + x = -17.435595774

Solving
-18 + x = -17.435595774

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 = -17.435595774 + 18

Combine like terms: -18 + 18 = 0
0 + x = -17.435595774 + 18
x = -17.435595774 + 18

Combine like terms: -17.435595774 + 18 = 0.564404226
x = 0.564404226

Simplifying
x = 0.564404226


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.435595774, 0.564404226}

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