x^2-800x+2400=0

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Solution for x^2-800x+2400=0 equation: 


Simplifying
x2 + -800x + 2400 = 0

Reorder the terms:
2400 + -800x + x2 = 0

Solving
2400 + -800x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2400' to each side of the equation.
2400 + -800x + -2400 + x2 = 0 + -2400

Reorder the terms:
2400 + -2400 + -800x + x2 = 0 + -2400

Combine like terms: 2400 + -2400 = 0
0 + -800x + x2 = 0 + -2400
-800x + x2 = 0 + -2400

Combine like terms: 0 + -2400 = -2400
-800x + x2 = -2400

The x term is -800x.  Take half its coefficient (-400).
Square it (160000) and add it to both sides.

Add '160000' to each side of the equation.
-800x + 160000 + x2 = -2400 + 160000

Reorder the terms:
160000 + -800x + x2 = -2400 + 160000

Combine like terms: -2400 + 160000 = 157600
160000 + -800x + x2 = 157600

Factor a perfect square on the left side:
(x + -400)(x + -400) = 157600

Calculate the square root of the right side: 396.988664826

Break this problem into two subproblems by setting 
(x + -400) equal to 396.988664826 and -396.988664826.


Subproblem 1
x + -400 = 396.988664826

Simplifying
x + -400 = 396.988664826

Reorder the terms:
-400 + x = 396.988664826

Solving
-400 + x = 396.988664826

Solving for variable 'x'.

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

Add '400' to each side of the equation.
-400 + 400 + x = 396.988664826 + 400

Combine like terms: -400 + 400 = 0
0 + x = 396.988664826 + 400
x = 396.988664826 + 400

Combine like terms: 396.988664826 + 400 = 796.988664826
x = 796.988664826

Simplifying
x = 796.988664826


Subproblem 2
x + -400 = -396.988664826

Simplifying
x + -400 = -396.988664826

Reorder the terms:
-400 + x = -396.988664826

Solving
-400 + x = -396.988664826

Solving for variable 'x'.

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

Add '400' to each side of the equation.
-400 + 400 + x = -396.988664826 + 400

Combine like terms: -400 + 400 = 0
0 + x = -396.988664826 + 400
x = -396.988664826 + 400

Combine like terms: -396.988664826 + 400 = 3.011335174
x = 3.011335174

Simplifying
x = 3.011335174


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {796.988664826, 3.011335174}

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