x^2-20x-480=0

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Solution for x^2-20x-480=0 equation: 


Simplifying
x2 + -20x + -480 = 0

Reorder the terms:
-480 + -20x + x2 = 0

Solving
-480 + -20x + 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 + -20x + 480 + x2 = 0 + 480

Reorder the terms:
-480 + 480 + -20x + x2 = 0 + 480

Combine like terms: -480 + 480 = 0
0 + -20x + x2 = 0 + 480
-20x + x2 = 0 + 480

Combine like terms: 0 + 480 = 480
-20x + x2 = 480

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 480 + 100

Reorder the terms:
100 + -20x + x2 = 480 + 100

Combine like terms: 480 + 100 = 580
100 + -20x + x2 = 580

Factor a perfect square on the left side:
(x + -10)(x + -10) = 580

Calculate the square root of the right side: 24.083189158

Break this problem into two subproblems by setting 
(x + -10) equal to 24.083189158 and -24.083189158.


Subproblem 1
x + -10 = 24.083189158

Simplifying
x + -10 = 24.083189158

Reorder the terms:
-10 + x = 24.083189158

Solving
-10 + x = 24.083189158

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 24.083189158 + 10

Combine like terms: -10 + 10 = 0
0 + x = 24.083189158 + 10
x = 24.083189158 + 10

Combine like terms: 24.083189158 + 10 = 34.083189158
x = 34.083189158

Simplifying
x = 34.083189158


Subproblem 2
x + -10 = -24.083189158

Simplifying
x + -10 = -24.083189158

Reorder the terms:
-10 + x = -24.083189158

Solving
-10 + x = -24.083189158

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -24.083189158 + 10

Combine like terms: -10 + 10 = 0
0 + x = -24.083189158 + 10
x = -24.083189158 + 10

Combine like terms: -24.083189158 + 10 = -14.083189158
x = -14.083189158

Simplifying
x = -14.083189158


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.083189158, -14.083189158}

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