x^2+2900x-1540000=0

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Solution for x^2+2900x-1540000=0 equation: 


Simplifying
x2 + 2900x + -1540000 = 0

Reorder the terms:
-1540000 + 2900x + x2 = 0

Solving
-1540000 + 2900x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1540000' to each side of the equation.
-1540000 + 2900x + 1540000 + x2 = 0 + 1540000

Reorder the terms:
-1540000 + 1540000 + 2900x + x2 = 0 + 1540000

Combine like terms: -1540000 + 1540000 = 0
0 + 2900x + x2 = 0 + 1540000
2900x + x2 = 0 + 1540000

Combine like terms: 0 + 1540000 = 1540000
2900x + x2 = 1540000

The x term is 2900x.  Take half its coefficient (1450).
Square it (2102500) and add it to both sides.

Add '2102500' to each side of the equation.
2900x + 2102500 + x2 = 1540000 + 2102500

Reorder the terms:
2102500 + 2900x + x2 = 1540000 + 2102500

Combine like terms: 1540000 + 2102500 = 3642500
2102500 + 2900x + x2 = 3642500

Factor a perfect square on the left side:
(x + 1450)(x + 1450) = 3642500

Calculate the square root of the right side: 1908.533468399

Break this problem into two subproblems by setting 
(x + 1450) equal to 1908.533468399 and -1908.533468399.


Subproblem 1
x + 1450 = 1908.533468399

Simplifying
x + 1450 = 1908.533468399

Reorder the terms:
1450 + x = 1908.533468399

Solving
1450 + x = 1908.533468399

Solving for variable 'x'.

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

Add '-1450' to each side of the equation.
1450 + -1450 + x = 1908.533468399 + -1450

Combine like terms: 1450 + -1450 = 0
0 + x = 1908.533468399 + -1450
x = 1908.533468399 + -1450

Combine like terms: 1908.533468399 + -1450 = 458.533468399
x = 458.533468399

Simplifying
x = 458.533468399


Subproblem 2
x + 1450 = -1908.533468399

Simplifying
x + 1450 = -1908.533468399

Reorder the terms:
1450 + x = -1908.533468399

Solving
1450 + x = -1908.533468399

Solving for variable 'x'.

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

Add '-1450' to each side of the equation.
1450 + -1450 + x = -1908.533468399 + -1450

Combine like terms: 1450 + -1450 = 0
0 + x = -1908.533468399 + -1450
x = -1908.533468399 + -1450

Combine like terms: -1908.533468399 + -1450 = -3358.533468399
x = -3358.533468399

Simplifying
x = -3358.533468399


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {458.533468399, -3358.533468399}

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