200x-x^2-6500+20x=

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Solution for 200x-x^2-6500+20x= equation:


Simplifying
200x + -1x2 + -6500 + 20x = 0

Reorder the terms:
-6500 + 200x + 20x + -1x2 = 0

Combine like terms: 200x + 20x = 220x
-6500 + 220x + -1x2 = 0

Solving
-6500 + 220x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
6500 + -220x + x2 = 0

Move the constant term to the right:

Add '-6500' to each side of the equation.
6500 + -220x + -6500 + x2 = 0 + -6500

Reorder the terms:
6500 + -6500 + -220x + x2 = 0 + -6500

Combine like terms: 6500 + -6500 = 0
0 + -220x + x2 = 0 + -6500
-220x + x2 = 0 + -6500

Combine like terms: 0 + -6500 = -6500
-220x + x2 = -6500

The x term is -220x.  Take half its coefficient (-110).
Square it (12100) and add it to both sides.

Add '12100' to each side of the equation.
-220x + 12100 + x2 = -6500 + 12100

Reorder the terms:
12100 + -220x + x2 = -6500 + 12100

Combine like terms: -6500 + 12100 = 5600
12100 + -220x + x2 = 5600

Factor a perfect square on the left side:
(x + -110)(x + -110) = 5600

Calculate the square root of the right side: 74.833147735

Break this problem into two subproblems by setting 
(x + -110) equal to 74.833147735 and -74.833147735.

Subproblem 1

x + -110 = 74.833147735 Simplifying x + -110 = 74.833147735 Reorder the terms: -110 + x = 74.833147735 Solving -110 + x = 74.833147735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = 74.833147735 + 110 Combine like terms: -110 + 110 = 0 0 + x = 74.833147735 + 110 x = 74.833147735 + 110 Combine like terms: 74.833147735 + 110 = 184.833147735 x = 184.833147735 Simplifying x = 184.833147735

Subproblem 2

x + -110 = -74.833147735 Simplifying x + -110 = -74.833147735 Reorder the terms: -110 + x = -74.833147735 Solving -110 + x = -74.833147735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = -74.833147735 + 110 Combine like terms: -110 + 110 = 0 0 + x = -74.833147735 + 110 x = -74.833147735 + 110 Combine like terms: -74.833147735 + 110 = 35.166852265 x = 35.166852265 Simplifying x = 35.166852265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {184.833147735, 35.166852265}

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