x^2+700x+40000=0

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Solution for x^2+700x+40000=0 equation: 


Simplifying
x2 + 700x + 40000 = 0

Reorder the terms:
40000 + 700x + x2 = 0

Solving
40000 + 700x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-40000' to each side of the equation.
40000 + 700x + -40000 + x2 = 0 + -40000

Reorder the terms:
40000 + -40000 + 700x + x2 = 0 + -40000

Combine like terms: 40000 + -40000 = 0
0 + 700x + x2 = 0 + -40000
700x + x2 = 0 + -40000

Combine like terms: 0 + -40000 = -40000
700x + x2 = -40000

The x term is 700x.  Take half its coefficient (350).
Square it (122500) and add it to both sides.

Add '122500' to each side of the equation.
700x + 122500 + x2 = -40000 + 122500

Reorder the terms:
122500 + 700x + x2 = -40000 + 122500

Combine like terms: -40000 + 122500 = 82500
122500 + 700x + x2 = 82500

Factor a perfect square on the left side:
(x + 350)(x + 350) = 82500

Calculate the square root of the right side: 287.228132327

Break this problem into two subproblems by setting 
(x + 350) equal to 287.228132327 and -287.228132327.


Subproblem 1
x + 350 = 287.228132327

Simplifying
x + 350 = 287.228132327

Reorder the terms:
350 + x = 287.228132327

Solving
350 + x = 287.228132327

Solving for variable 'x'.

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

Add '-350' to each side of the equation.
350 + -350 + x = 287.228132327 + -350

Combine like terms: 350 + -350 = 0
0 + x = 287.228132327 + -350
x = 287.228132327 + -350

Combine like terms: 287.228132327 + -350 = -62.771867673
x = -62.771867673

Simplifying
x = -62.771867673


Subproblem 2
x + 350 = -287.228132327

Simplifying
x + 350 = -287.228132327

Reorder the terms:
350 + x = -287.228132327

Solving
350 + x = -287.228132327

Solving for variable 'x'.

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

Add '-350' to each side of the equation.
350 + -350 + x = -287.228132327 + -350

Combine like terms: 350 + -350 = 0
0 + x = -287.228132327 + -350
x = -287.228132327 + -350

Combine like terms: -287.228132327 + -350 = -637.228132327
x = -637.228132327

Simplifying
x = -637.228132327


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-62.771867673, -637.228132327}

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