x^2-20x-280=0

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Solution for x^2-20x-280=0 equation: 


Simplifying
x2 + -20x + -280 = 0

Reorder the terms:
-280 + -20x + x2 = 0

Solving
-280 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + -20x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + -20x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + -20x + x2 = 0 + 280
-20x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
-20x + x2 = 280

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 = 280 + 100

Reorder the terms:
100 + -20x + x2 = 280 + 100

Combine like terms: 280 + 100 = 380
100 + -20x + x2 = 380

Factor a perfect square on the left side:
(x + -10)(x + -10) = 380

Calculate the square root of the right side: 19.49358869

Break this problem into two subproblems by setting 
(x + -10) equal to 19.49358869 and -19.49358869.


Subproblem 1
x + -10 = 19.49358869

Simplifying
x + -10 = 19.49358869

Reorder the terms:
-10 + x = 19.49358869

Solving
-10 + x = 19.49358869

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 = 19.49358869 + 10

Combine like terms: -10 + 10 = 0
0 + x = 19.49358869 + 10
x = 19.49358869 + 10

Combine like terms: 19.49358869 + 10 = 29.49358869
x = 29.49358869

Simplifying
x = 29.49358869


Subproblem 2
x + -10 = -19.49358869

Simplifying
x + -10 = -19.49358869

Reorder the terms:
-10 + x = -19.49358869

Solving
-10 + x = -19.49358869

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 = -19.49358869 + 10

Combine like terms: -10 + 10 = 0
0 + x = -19.49358869 + 10
x = -19.49358869 + 10

Combine like terms: -19.49358869 + 10 = -9.49358869
x = -9.49358869

Simplifying
x = -9.49358869


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.49358869, -9.49358869}

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