x^2+4840x+5248000=1219200

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Solution for x^2+4840x+5248000=1219200 equation: 


Simplifying
x2 + 4840x + 5248000 = 1219200

Reorder the terms:
5248000 + 4840x + x2 = 1219200

Solving
5248000 + 4840x + x2 = 1219200

Solving for variable 'x'.

Reorder the terms:
5248000 + -1219200 + 4840x + x2 = 1219200 + -1219200

Combine like terms: 5248000 + -1219200 = 4028800
4028800 + 4840x + x2 = 1219200 + -1219200

Combine like terms: 1219200 + -1219200 = 0
4028800 + 4840x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4028800' to each side of the equation.
4028800 + 4840x + -4028800 + x2 = 0 + -4028800

Reorder the terms:
4028800 + -4028800 + 4840x + x2 = 0 + -4028800

Combine like terms: 4028800 + -4028800 = 0
0 + 4840x + x2 = 0 + -4028800
4840x + x2 = 0 + -4028800

Combine like terms: 0 + -4028800 = -4028800
4840x + x2 = -4028800

The x term is 4840x.  Take half its coefficient (2420).
Square it (5856400) and add it to both sides.

Add '5856400' to each side of the equation.
4840x + 5856400 + x2 = -4028800 + 5856400

Reorder the terms:
5856400 + 4840x + x2 = -4028800 + 5856400

Combine like terms: -4028800 + 5856400 = 1827600
5856400 + 4840x + x2 = 1827600

Factor a perfect square on the left side:
(x + 2420)(x + 2420) = 1827600

Calculate the square root of the right side: 1351.88756929

Break this problem into two subproblems by setting 
(x + 2420) equal to 1351.88756929 and -1351.88756929.


Subproblem 1
x + 2420 = 1351.88756929

Simplifying
x + 2420 = 1351.88756929

Reorder the terms:
2420 + x = 1351.88756929

Solving
2420 + x = 1351.88756929

Solving for variable 'x'.

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

Add '-2420' to each side of the equation.
2420 + -2420 + x = 1351.88756929 + -2420

Combine like terms: 2420 + -2420 = 0
0 + x = 1351.88756929 + -2420
x = 1351.88756929 + -2420

Combine like terms: 1351.88756929 + -2420 = -1068.11243071
x = -1068.11243071

Simplifying
x = -1068.11243071


Subproblem 2
x + 2420 = -1351.88756929

Simplifying
x + 2420 = -1351.88756929

Reorder the terms:
2420 + x = -1351.88756929

Solving
2420 + x = -1351.88756929

Solving for variable 'x'.

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

Add '-2420' to each side of the equation.
2420 + -2420 + x = -1351.88756929 + -2420

Combine like terms: 2420 + -2420 = 0
0 + x = -1351.88756929 + -2420
x = -1351.88756929 + -2420

Combine like terms: -1351.88756929 + -2420 = -3771.88756929
x = -3771.88756929

Simplifying
x = -3771.88756929


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1068.11243071, -3771.88756929}

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