-.5x^2+200x-4800=0

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Solution for -.5x^2+200x-4800=0 equation: 


Simplifying
-0.5x2 + 200x + -4800 = 0

Reorder the terms:
-4800 + 200x + -0.5x2 = 0

Solving
-4800 + 200x + -0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
9600 + -400x + x2 = 0

Move the constant term to the right:

Add '-9600' to each side of the equation.
9600 + -400x + -9600 + x2 = 0 + -9600

Reorder the terms:
9600 + -9600 + -400x + x2 = 0 + -9600

Combine like terms: 9600 + -9600 = 0
0 + -400x + x2 = 0 + -9600
-400x + x2 = 0 + -9600

Combine like terms: 0 + -9600 = -9600
-400x + x2 = -9600

The x term is -400x.  Take half its coefficient (-200).
Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.
-400x + 40000 + x2 = -9600 + 40000

Reorder the terms:
40000 + -400x + x2 = -9600 + 40000

Combine like terms: -9600 + 40000 = 30400
40000 + -400x + x2 = 30400

Factor a perfect square on the left side:
(x + -200)(x + -200) = 30400

Calculate the square root of the right side: 174.355957742

Break this problem into two subproblems by setting 
(x + -200) equal to 174.355957742 and -174.355957742.


Subproblem 1
x + -200 = 174.355957742

Simplifying
x + -200 = 174.355957742

Reorder the terms:
-200 + x = 174.355957742

Solving
-200 + x = 174.355957742

Solving for variable 'x'.

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

Add '200' to each side of the equation.
-200 + 200 + x = 174.355957742 + 200

Combine like terms: -200 + 200 = 0
0 + x = 174.355957742 + 200
x = 174.355957742 + 200

Combine like terms: 174.355957742 + 200 = 374.355957742
x = 374.355957742

Simplifying
x = 374.355957742


Subproblem 2
x + -200 = -174.355957742

Simplifying
x + -200 = -174.355957742

Reorder the terms:
-200 + x = -174.355957742

Solving
-200 + x = -174.355957742

Solving for variable 'x'.

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

Add '200' to each side of the equation.
-200 + 200 + x = -174.355957742 + 200

Combine like terms: -200 + 200 = 0
0 + x = -174.355957742 + 200
x = -174.355957742 + 200

Combine like terms: -174.355957742 + 200 = 25.644042258
x = 25.644042258

Simplifying
x = 25.644042258


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {374.355957742, 25.644042258}

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