x^2+1200x+2400=0

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Solution for x^2+1200x+2400=0 equation:


Simplifying
x2 + 1200x + 2400 = 0

Reorder the terms:
2400 + 1200x + x2 = 0

Solving
2400 + 1200x + 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 + 1200x + -2400 + x2 = 0 + -2400

Reorder the terms:
2400 + -2400 + 1200x + x2 = 0 + -2400

Combine like terms: 2400 + -2400 = 0
0 + 1200x + x2 = 0 + -2400
1200x + x2 = 0 + -2400

Combine like terms: 0 + -2400 = -2400
1200x + x2 = -2400

The x term is 1200x.  Take half its coefficient (600).
Square it (360000) and add it to both sides.

Add '360000' to each side of the equation.
1200x + 360000 + x2 = -2400 + 360000

Reorder the terms:
360000 + 1200x + x2 = -2400 + 360000

Combine like terms: -2400 + 360000 = 357600
360000 + 1200x + x2 = 357600

Factor a perfect square on the left side:
(x + 600)(x + 600) = 357600

Calculate the square root of the right side: 597.996655509

Break this problem into two subproblems by setting 
(x + 600) equal to 597.996655509 and -597.996655509.


Subproblem 1
x + 600 = 597.996655509

Simplifying
x + 600 = 597.996655509

Reorder the terms:
600 + x = 597.996655509

Solving
600 + x = 597.996655509

Solving for variable 'x'.

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

Add '-600' to each side of the equation.
600 + -600 + x = 597.996655509 + -600

Combine like terms: 600 + -600 = 0
0 + x = 597.996655509 + -600
x = 597.996655509 + -600

Combine like terms: 597.996655509 + -600 = -2.003344491
x = -2.003344491

Simplifying
x = -2.003344491


Subproblem 2
x + 600 = -597.996655509

Simplifying
x + 600 = -597.996655509

Reorder the terms:
600 + x = -597.996655509

Solving
600 + x = -597.996655509

Solving for variable 'x'.

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

Add '-600' to each side of the equation.
600 + -600 + x = -597.996655509 + -600

Combine like terms: 600 + -600 = 0
0 + x = -597.996655509 + -600
x = -597.996655509 + -600

Combine like terms: -597.996655509 + -600 = -1197.996655509
x = -1197.996655509

Simplifying
x = -1197.996655509


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.003344491, -1197.996655509}

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