x^2-40x+360=0

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Solution for x^2-40x+360=0 equation: 


Simplifying
x2 + -40x + 360 = 0

Reorder the terms:
360 + -40x + x2 = 0

Solving
360 + -40x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-360' to each side of the equation.
360 + -40x + -360 + x2 = 0 + -360

Reorder the terms:
360 + -360 + -40x + x2 = 0 + -360

Combine like terms: 360 + -360 = 0
0 + -40x + x2 = 0 + -360
-40x + x2 = 0 + -360

Combine like terms: 0 + -360 = -360
-40x + x2 = -360

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -360 + 400

Reorder the terms:
400 + -40x + x2 = -360 + 400

Combine like terms: -360 + 400 = 40
400 + -40x + x2 = 40

Factor a perfect square on the left side:
(x + -20)(x + -20) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -20) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -20 = 6.32455532

Simplifying
x + -20 = 6.32455532

Reorder the terms:
-20 + x = 6.32455532

Solving
-20 + x = 6.32455532

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20' to each side of the equation.
-20 + 20 + x = 6.32455532 + 20

Combine like terms: -20 + 20 = 0
0 + x = 6.32455532 + 20
x = 6.32455532 + 20

Combine like terms: 6.32455532 + 20 = 26.32455532
x = 26.32455532

Simplifying
x = 26.32455532


Subproblem 2
x + -20 = -6.32455532

Simplifying
x + -20 = -6.32455532

Reorder the terms:
-20 + x = -6.32455532

Solving
-20 + x = -6.32455532

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20' to each side of the equation.
-20 + 20 + x = -6.32455532 + 20

Combine like terms: -20 + 20 = 0
0 + x = -6.32455532 + 20
x = -6.32455532 + 20

Combine like terms: -6.32455532 + 20 = 13.67544468
x = 13.67544468

Simplifying
x = 13.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.32455532, 13.67544468}

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