100+2x+0.0025x^2=0

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Solution for 100+2x+0.0025x^2=0 equation: 


Simplifying
100 + 2x + 0.0025x2 = 0

Solving
100 + 2x + 0.0025x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0025 the coefficient of the squared term: 

Divide each side by '0.0025'.
40000 + 800x + x2 = 0

Move the constant term to the right:

Add '-40000' to each side of the equation.
40000 + 800x + -40000 + x2 = 0 + -40000

Reorder the terms:
40000 + -40000 + 800x + x2 = 0 + -40000

Combine like terms: 40000 + -40000 = 0
0 + 800x + x2 = 0 + -40000
800x + x2 = 0 + -40000

Combine like terms: 0 + -40000 = -40000
800x + x2 = -40000

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 = -40000 + 160000

Reorder the terms:
160000 + 800x + x2 = -40000 + 160000

Combine like terms: -40000 + 160000 = 120000
160000 + 800x + x2 = 120000

Factor a perfect square on the left side:
(x + 400)(x + 400) = 120000

Calculate the square root of the right side: 346.410161514

Break this problem into two subproblems by setting 
(x + 400) equal to 346.410161514 and -346.410161514.


Subproblem 1
x + 400 = 346.410161514

Simplifying
x + 400 = 346.410161514

Reorder the terms:
400 + x = 346.410161514

Solving
400 + x = 346.410161514

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 = 346.410161514 + -400

Combine like terms: 400 + -400 = 0
0 + x = 346.410161514 + -400
x = 346.410161514 + -400

Combine like terms: 346.410161514 + -400 = -53.589838486
x = -53.589838486

Simplifying
x = -53.589838486


Subproblem 2
x + 400 = -346.410161514

Simplifying
x + 400 = -346.410161514

Reorder the terms:
400 + x = -346.410161514

Solving
400 + x = -346.410161514

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 = -346.410161514 + -400

Combine like terms: 400 + -400 = 0
0 + x = -346.410161514 + -400
x = -346.410161514 + -400

Combine like terms: -346.410161514 + -400 = -746.410161514
x = -746.410161514

Simplifying
x = -746.410161514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-53.589838486, -746.410161514}

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