-.2x^2+90x-2000=0

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Solution for -.2x^2+90x-2000=0 equation: 


Simplifying
-0.2x2 + 90x + -2000 = 0

Reorder the terms:
-2000 + 90x + -0.2x2 = 0

Solving
-2000 + 90x + -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'.
10000 + -450x + x2 = 0

Move the constant term to the right:

Add '-10000' to each side of the equation.
10000 + -450x + -10000 + x2 = 0 + -10000

Reorder the terms:
10000 + -10000 + -450x + x2 = 0 + -10000

Combine like terms: 10000 + -10000 = 0
0 + -450x + x2 = 0 + -10000
-450x + x2 = 0 + -10000

Combine like terms: 0 + -10000 = -10000
-450x + x2 = -10000

The x term is -450x.  Take half its coefficient (-225).
Square it (50625) and add it to both sides.

Add '50625' to each side of the equation.
-450x + 50625 + x2 = -10000 + 50625

Reorder the terms:
50625 + -450x + x2 = -10000 + 50625

Combine like terms: -10000 + 50625 = 40625
50625 + -450x + x2 = 40625

Factor a perfect square on the left side:
(x + -225)(x + -225) = 40625

Calculate the square root of the right side: 201.556443707

Break this problem into two subproblems by setting 
(x + -225) equal to 201.556443707 and -201.556443707.


Subproblem 1
x + -225 = 201.556443707

Simplifying
x + -225 = 201.556443707

Reorder the terms:
-225 + x = 201.556443707

Solving
-225 + x = 201.556443707

Solving for variable 'x'.

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

Add '225' to each side of the equation.
-225 + 225 + x = 201.556443707 + 225

Combine like terms: -225 + 225 = 0
0 + x = 201.556443707 + 225
x = 201.556443707 + 225

Combine like terms: 201.556443707 + 225 = 426.556443707
x = 426.556443707

Simplifying
x = 426.556443707


Subproblem 2
x + -225 = -201.556443707

Simplifying
x + -225 = -201.556443707

Reorder the terms:
-225 + x = -201.556443707

Solving
-225 + x = -201.556443707

Solving for variable 'x'.

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

Add '225' to each side of the equation.
-225 + 225 + x = -201.556443707 + 225

Combine like terms: -225 + 225 = 0
0 + x = -201.556443707 + 225
x = -201.556443707 + 225

Combine like terms: -201.556443707 + 225 = 23.443556293
x = 23.443556293

Simplifying
x = 23.443556293


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {426.556443707, 23.443556293}

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