200(x)=-2x^2+40x+100

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Solution for 200(x)=-2x^2+40x+100 equation: 


Simplifying
200(x) = -2x2 + 40x + 100

Reorder the terms:
200x = 100 + 40x + -2x2

Solving
200x = 100 + 40x + -2x2

Solving for variable 'x'.

Reorder the terms:
-100 + 200x + -40x + 2x2 = 100 + 40x + -2x2 + -100 + -40x + 2x2

Combine like terms: 200x + -40x = 160x
-100 + 160x + 2x2 = 100 + 40x + -2x2 + -100 + -40x + 2x2

Reorder the terms:
-100 + 160x + 2x2 = 100 + -100 + 40x + -40x + -2x2 + 2x2

Combine like terms: 100 + -100 = 0
-100 + 160x + 2x2 = 0 + 40x + -40x + -2x2 + 2x2
-100 + 160x + 2x2 = 40x + -40x + -2x2 + 2x2

Combine like terms: 40x + -40x = 0
-100 + 160x + 2x2 = 0 + -2x2 + 2x2
-100 + 160x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-100 + 160x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 80x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 80x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + 80x + x2 = 0

Solving
-50 + 80x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 80x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 80x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 80x + x2 = 0 + 50
80x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
80x + x2 = 50

The x term is 80x.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80x + 1600 + x2 = 50 + 1600

Reorder the terms:
1600 + 80x + x2 = 50 + 1600

Combine like terms: 50 + 1600 = 1650
1600 + 80x + x2 = 1650

Factor a perfect square on the left side:
(x + 40)(x + 40) = 1650

Calculate the square root of the right side: 40.620192023

Break this problem into two subproblems by setting 
(x + 40) equal to 40.620192023 and -40.620192023.


Subproblem 1
x + 40 = 40.620192023

Simplifying
x + 40 = 40.620192023

Reorder the terms:
40 + x = 40.620192023

Solving
40 + x = 40.620192023

Solving for variable 'x'.

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

Add '-40' to each side of the equation.
40 + -40 + x = 40.620192023 + -40

Combine like terms: 40 + -40 = 0
0 + x = 40.620192023 + -40
x = 40.620192023 + -40

Combine like terms: 40.620192023 + -40 = 0.620192023
x = 0.620192023

Simplifying
x = 0.620192023


Subproblem 2
x + 40 = -40.620192023

Simplifying
x + 40 = -40.620192023

Reorder the terms:
40 + x = -40.620192023

Solving
40 + x = -40.620192023

Solving for variable 'x'.

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

Add '-40' to each side of the equation.
40 + -40 + x = -40.620192023 + -40

Combine like terms: 40 + -40 = 0
0 + x = -40.620192023 + -40
x = -40.620192023 + -40

Combine like terms: -40.620192023 + -40 = -80.620192023
x = -80.620192023

Simplifying
x = -80.620192023


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.620192023, -80.620192023}
Solution
x = {0.620192023, -80.620192023}

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