-0.2x^2+85x-1500=0

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Solution for -0.2x^2+85x-1500=0 equation: 


Simplifying
-0.2x2 + 85x + -1500 = 0

Reorder the terms:
-1500 + 85x + -0.2x2 = 0

Solving
-1500 + 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'.
7500 + -425x + x2 = 0

Move the constant term to the right:

Add '-7500' to each side of the equation.
7500 + -425x + -7500 + x2 = 0 + -7500

Reorder the terms:
7500 + -7500 + -425x + x2 = 0 + -7500

Combine like terms: 7500 + -7500 = 0
0 + -425x + x2 = 0 + -7500
-425x + x2 = 0 + -7500

Combine like terms: 0 + -7500 = -7500
-425x + x2 = -7500

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 = -7500 + 45156.25

Reorder the terms:
45156.25 + -425x + x2 = -7500 + 45156.25

Combine like terms: -7500 + 45156.25 = 37656.25
45156.25 + -425x + x2 = 37656.25

Factor a perfect square on the left side:
(x + -212.5)(x + -212.5) = 37656.25

Calculate the square root of the right side: 194.052183703

Break this problem into two subproblems by setting 
(x + -212.5) equal to 194.052183703 and -194.052183703.


Subproblem 1
x + -212.5 = 194.052183703

Simplifying
x + -212.5 = 194.052183703

Reorder the terms:
-212.5 + x = 194.052183703

Solving
-212.5 + x = 194.052183703

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 = 194.052183703 + 212.5

Combine like terms: -212.5 + 212.5 = 0.0
0.0 + x = 194.052183703 + 212.5
x = 194.052183703 + 212.5

Combine like terms: 194.052183703 + 212.5 = 406.552183703
x = 406.552183703

Simplifying
x = 406.552183703


Subproblem 2
x + -212.5 = -194.052183703

Simplifying
x + -212.5 = -194.052183703

Reorder the terms:
-212.5 + x = -194.052183703

Solving
-212.5 + x = -194.052183703

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 = -194.052183703 + 212.5

Combine like terms: -212.5 + 212.5 = 0.0
0.0 + x = -194.052183703 + 212.5
x = -194.052183703 + 212.5

Combine like terms: -194.052183703 + 212.5 = 18.447816297
x = 18.447816297

Simplifying
x = 18.447816297


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {406.552183703, 18.447816297}

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