x^2-88x+480=0

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Solution for x^2-88x+480=0 equation: 


Simplifying
x2 + -88x + 480 = 0

Reorder the terms:
480 + -88x + x2 = 0

Solving
480 + -88x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-480' to each side of the equation.
480 + -88x + -480 + x2 = 0 + -480

Reorder the terms:
480 + -480 + -88x + x2 = 0 + -480

Combine like terms: 480 + -480 = 0
0 + -88x + x2 = 0 + -480
-88x + x2 = 0 + -480

Combine like terms: 0 + -480 = -480
-88x + x2 = -480

The x term is -88x.  Take half its coefficient (-44).
Square it (1936) and add it to both sides.

Add '1936' to each side of the equation.
-88x + 1936 + x2 = -480 + 1936

Reorder the terms:
1936 + -88x + x2 = -480 + 1936

Combine like terms: -480 + 1936 = 1456
1936 + -88x + x2 = 1456

Factor a perfect square on the left side:
(x + -44)(x + -44) = 1456

Calculate the square root of the right side: 38.157568057

Break this problem into two subproblems by setting 
(x + -44) equal to 38.157568057 and -38.157568057.


Subproblem 1
x + -44 = 38.157568057

Simplifying
x + -44 = 38.157568057

Reorder the terms:
-44 + x = 38.157568057

Solving
-44 + x = 38.157568057

Solving for variable 'x'.

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

Add '44' to each side of the equation.
-44 + 44 + x = 38.157568057 + 44

Combine like terms: -44 + 44 = 0
0 + x = 38.157568057 + 44
x = 38.157568057 + 44

Combine like terms: 38.157568057 + 44 = 82.157568057
x = 82.157568057

Simplifying
x = 82.157568057


Subproblem 2
x + -44 = -38.157568057

Simplifying
x + -44 = -38.157568057

Reorder the terms:
-44 + x = -38.157568057

Solving
-44 + x = -38.157568057

Solving for variable 'x'.

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

Add '44' to each side of the equation.
-44 + 44 + x = -38.157568057 + 44

Combine like terms: -44 + 44 = 0
0 + x = -38.157568057 + 44
x = -38.157568057 + 44

Combine like terms: -38.157568057 + 44 = 5.842431943
x = 5.842431943

Simplifying
x = 5.842431943


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {82.157568057, 5.842431943}

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