x^2-36x+192=0

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Solution for x^2-36x+192=0 equation: 


Simplifying
x2 + -36x + 192 = 0

Reorder the terms:
192 + -36x + x2 = 0

Solving
192 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-192' to each side of the equation.
192 + -36x + -192 + x2 = 0 + -192

Reorder the terms:
192 + -192 + -36x + x2 = 0 + -192

Combine like terms: 192 + -192 = 0
0 + -36x + x2 = 0 + -192
-36x + x2 = 0 + -192

Combine like terms: 0 + -192 = -192
-36x + x2 = -192

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 = -192 + 324

Reorder the terms:
324 + -36x + x2 = -192 + 324

Combine like terms: -192 + 324 = 132
324 + -36x + x2 = 132

Factor a perfect square on the left side:
(x + -18)(x + -18) = 132

Calculate the square root of the right side: 11.489125293

Break this problem into two subproblems by setting 
(x + -18) equal to 11.489125293 and -11.489125293.


Subproblem 1
x + -18 = 11.489125293

Simplifying
x + -18 = 11.489125293

Reorder the terms:
-18 + x = 11.489125293

Solving
-18 + x = 11.489125293

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 = 11.489125293 + 18

Combine like terms: -18 + 18 = 0
0 + x = 11.489125293 + 18
x = 11.489125293 + 18

Combine like terms: 11.489125293 + 18 = 29.489125293
x = 29.489125293

Simplifying
x = 29.489125293


Subproblem 2
x + -18 = -11.489125293

Simplifying
x + -18 = -11.489125293

Reorder the terms:
-18 + x = -11.489125293

Solving
-18 + x = -11.489125293

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 = -11.489125293 + 18

Combine like terms: -18 + 18 = 0
0 + x = -11.489125293 + 18
x = -11.489125293 + 18

Combine like terms: -11.489125293 + 18 = 6.510874707
x = 6.510874707

Simplifying
x = 6.510874707


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.489125293, 6.510874707}

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