200=-5x^2+100x

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Solution for 200=-5x^2+100x equation: 


Simplifying
200 = -5x2 + 100x

Reorder the terms:
200 = 100x + -5x2

Solving
200 = 100x + -5x2

Solving for variable 'x'.

Reorder the terms:
200 + -100x + 5x2 = 100x + -100x + -5x2 + 5x2

Combine like terms: 100x + -100x = 0
200 + -100x + 5x2 = 0 + -5x2 + 5x2
200 + -100x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
200 + -100x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(40 + -20x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(40 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
40 + -20x + x2 = 0

Solving
40 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -20x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + -20x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -20x + x2 = 0 + -40
-20x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
-20x + x2 = -40

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -40 + 100

Reorder the terms:
100 + -20x + x2 = -40 + 100

Combine like terms: -40 + 100 = 60
100 + -20x + x2 = 60

Factor a perfect square on the left side:
(x + -10)(x + -10) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + -10) equal to 7.745966692 and -7.745966692.


Subproblem 1
x + -10 = 7.745966692

Simplifying
x + -10 = 7.745966692

Reorder the terms:
-10 + x = 7.745966692

Solving
-10 + x = 7.745966692

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 7.745966692 + 10

Combine like terms: -10 + 10 = 0
0 + x = 7.745966692 + 10
x = 7.745966692 + 10

Combine like terms: 7.745966692 + 10 = 17.745966692
x = 17.745966692

Simplifying
x = 17.745966692


Subproblem 2
x + -10 = -7.745966692

Simplifying
x + -10 = -7.745966692

Reorder the terms:
-10 + x = -7.745966692

Solving
-10 + x = -7.745966692

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -7.745966692 + 10

Combine like terms: -10 + 10 = 0
0 + x = -7.745966692 + 10
x = -7.745966692 + 10

Combine like terms: -7.745966692 + 10 = 2.254033308
x = 2.254033308

Simplifying
x = 2.254033308


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.745966692, 2.254033308}
Solution
x = {17.745966692, 2.254033308}

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