x^2-280x-2700=0

Solution for x^2-280x-2700=0 equation:

Simplifying
x2 + -280x + -2700 = 0

Reorder the terms:
-2700 + -280x + x2 = 0

Solving
-2700 + -280x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2700' to each side of the equation.
-2700 + -280x + 2700 + x2 = 0 + 2700

Reorder the terms:
-2700 + 2700 + -280x + x2 = 0 + 2700

Combine like terms: -2700 + 2700 = 0
0 + -280x + x2 = 0 + 2700
-280x + x2 = 0 + 2700

Combine like terms: 0 + 2700 = 2700
-280x + x2 = 2700

The x term is -280x.  Take half its coefficient (-140).
Square it (19600) and add it to both sides.

Add '19600' to each side of the equation.
-280x + 19600 + x2 = 2700 + 19600

Reorder the terms:
19600 + -280x + x2 = 2700 + 19600

Combine like terms: 2700 + 19600 = 22300
19600 + -280x + x2 = 22300

Factor a perfect square on the left side:
(x + -140)(x + -140) = 22300

Calculate the square root of the right side: 149.331845231

Break this problem into two subproblems by setting 
(x + -140) equal to 149.331845231 and -149.331845231.

Subproblem 1
x + -140 = 149.331845231

Simplifying
x + -140 = 149.331845231

Reorder the terms:
-140 + x = 149.331845231

Solving
-140 + x = 149.331845231

Solving for variable 'x'.

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

Add '140' to each side of the equation.
-140 + 140 + x = 149.331845231 + 140

Combine like terms: -140 + 140 = 0
0 + x = 149.331845231 + 140
x = 149.331845231 + 140

Combine like terms: 149.331845231 + 140 = 289.331845231
x = 289.331845231

Simplifying
x = 289.331845231

Subproblem 2
x + -140 = -149.331845231

Simplifying
x + -140 = -149.331845231

Reorder the terms:
-140 + x = -149.331845231

Solving
-140 + x = -149.331845231

Solving for variable 'x'.

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

Add '140' to each side of the equation.
-140 + 140 + x = -149.331845231 + 140

Combine like terms: -140 + 140 = 0
0 + x = -149.331845231 + 140
x = -149.331845231 + 140

Combine like terms: -149.331845231 + 140 = -9.331845231
x = -9.331845231

Simplifying
x = -9.331845231

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {289.331845231, -9.331845231}