x^2-72x-320=0

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Solution for x^2-72x-320=0 equation: 


Simplifying
x2 + -72x + -320 = 0

Reorder the terms:
-320 + -72x + x2 = 0

Solving
-320 + -72x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + -72x + 320 + x2 = 0 + 320

Reorder the terms:
-320 + 320 + -72x + x2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + -72x + x2 = 0 + 320
-72x + x2 = 0 + 320

Combine like terms: 0 + 320 = 320
-72x + x2 = 320

The x term is -72x.  Take half its coefficient (-36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
-72x + 1296 + x2 = 320 + 1296

Reorder the terms:
1296 + -72x + x2 = 320 + 1296

Combine like terms: 320 + 1296 = 1616
1296 + -72x + x2 = 1616

Factor a perfect square on the left side:
(x + -36)(x + -36) = 1616

Calculate the square root of the right side: 40.199502484

Break this problem into two subproblems by setting 
(x + -36) equal to 40.199502484 and -40.199502484.


Subproblem 1
x + -36 = 40.199502484

Simplifying
x + -36 = 40.199502484

Reorder the terms:
-36 + x = 40.199502484

Solving
-36 + x = 40.199502484

Solving for variable 'x'.

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

Add '36' to each side of the equation.
-36 + 36 + x = 40.199502484 + 36

Combine like terms: -36 + 36 = 0
0 + x = 40.199502484 + 36
x = 40.199502484 + 36

Combine like terms: 40.199502484 + 36 = 76.199502484
x = 76.199502484

Simplifying
x = 76.199502484


Subproblem 2
x + -36 = -40.199502484

Simplifying
x + -36 = -40.199502484

Reorder the terms:
-36 + x = -40.199502484

Solving
-36 + x = -40.199502484

Solving for variable 'x'.

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

Add '36' to each side of the equation.
-36 + 36 + x = -40.199502484 + 36

Combine like terms: -36 + 36 = 0
0 + x = -40.199502484 + 36
x = -40.199502484 + 36

Combine like terms: -40.199502484 + 36 = -4.199502484
x = -4.199502484

Simplifying
x = -4.199502484


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {76.199502484, -4.199502484}

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