0.2x^2+85x+2500=0

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Solution for 0.2x^2+85x+2500=0 equation: 


Simplifying
0.2x2 + 85x + 2500 = 0

Reorder the terms:
2500 + 85x + 0.2x2 = 0

Solving
2500 + 85x + 0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.2'.
12500 + 425x + x2 = 0

Move the constant term to the right:

Add '-12500' to each side of the equation.
12500 + 425x + -12500 + x2 = 0 + -12500

Reorder the terms:
12500 + -12500 + 425x + x2 = 0 + -12500

Combine like terms: 12500 + -12500 = 0
0 + 425x + x2 = 0 + -12500
425x + x2 = 0 + -12500

Combine like terms: 0 + -12500 = -12500
425x + x2 = -12500

The x term is 425x.  Take half its coefficient (212.5).
Square it (45156.25) and add it to both sides.

Add '45156.25' to each side of the equation.
425x + 45156.25 + x2 = -12500 + 45156.25

Reorder the terms:
45156.25 + 425x + x2 = -12500 + 45156.25

Combine like terms: -12500 + 45156.25 = 32656.25
45156.25 + 425x + x2 = 32656.25

Factor a perfect square on the left side:
(x + 212.5)(x + 212.5) = 32656.25

Calculate the square root of the right side: 180.710403685

Break this problem into two subproblems by setting 
(x + 212.5) equal to 180.710403685 and -180.710403685.


Subproblem 1
x + 212.5 = 180.710403685

Simplifying
x + 212.5 = 180.710403685

Reorder the terms:
212.5 + x = 180.710403685

Solving
212.5 + x = 180.710403685

Solving for variable 'x'.

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

Add '-212.5' to each side of the equation.
212.5 + -212.5 + x = 180.710403685 + -212.5

Combine like terms: 212.5 + -212.5 = 0.0
0.0 + x = 180.710403685 + -212.5
x = 180.710403685 + -212.5

Combine like terms: 180.710403685 + -212.5 = -31.789596315
x = -31.789596315

Simplifying
x = -31.789596315


Subproblem 2
x + 212.5 = -180.710403685

Simplifying
x + 212.5 = -180.710403685

Reorder the terms:
212.5 + x = -180.710403685

Solving
212.5 + x = -180.710403685

Solving for variable 'x'.

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

Add '-212.5' to each side of the equation.
212.5 + -212.5 + x = -180.710403685 + -212.5

Combine like terms: 212.5 + -212.5 = 0.0
0.0 + x = -180.710403685 + -212.5
x = -180.710403685 + -212.5

Combine like terms: -180.710403685 + -212.5 = -393.210403685
x = -393.210403685

Simplifying
x = -393.210403685


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-31.789596315, -393.210403685}

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