100x-x^2=200

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


Simplifying
100x + -1x2 = 200

Solving
100x + -1x2 = 200

Solving for variable 'x'.

Reorder the terms:
-200 + 100x + -1x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-200 + 100x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
200 + -100x + x2 = 0

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -100x + -200 + x2 = 0 + -200

Reorder the terms:
200 + -200 + -100x + x2 = 0 + -200

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

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

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = -200 + 2500

Reorder the terms:
2500 + -100x + x2 = -200 + 2500

Combine like terms: -200 + 2500 = 2300
2500 + -100x + x2 = 2300

Factor a perfect square on the left side:
(x + -50)(x + -50) = 2300

Calculate the square root of the right side: 47.958315233

Break this problem into two subproblems by setting 
(x + -50) equal to 47.958315233 and -47.958315233.

Subproblem 1

x + -50 = 47.958315233 Simplifying x + -50 = 47.958315233 Reorder the terms: -50 + x = 47.958315233 Solving -50 + x = 47.958315233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 47.958315233 + 50 Combine like terms: -50 + 50 = 0 0 + x = 47.958315233 + 50 x = 47.958315233 + 50 Combine like terms: 47.958315233 + 50 = 97.958315233 x = 97.958315233 Simplifying x = 97.958315233

Subproblem 2

x + -50 = -47.958315233 Simplifying x + -50 = -47.958315233 Reorder the terms: -50 + x = -47.958315233 Solving -50 + x = -47.958315233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -47.958315233 + 50 Combine like terms: -50 + 50 = 0 0 + x = -47.958315233 + 50 x = -47.958315233 + 50 Combine like terms: -47.958315233 + 50 = 2.041684767 x = 2.041684767 Simplifying x = 2.041684767

Solution

The solution to the problem is based on the solutions from the subproblems. x = {97.958315233, 2.041684767}

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