20000=300x-x^2

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Solution for 20000=300x-x^2 equation:


Simplifying
20000 = 300x + -1x2

Solving
20000 = 300x + -1x2

Solving for variable 'x'.

Reorder the terms:
20000 + -300x + x2 = 300x + -300x + -1x2 + x2

Combine like terms: 300x + -300x = 0
20000 + -300x + x2 = 0 + -1x2 + x2
20000 + -300x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
20000 + -300x + x2 = 0

Factor a trinomial.
(100 + -1x)(200 + -1x) = 0

Subproblem 1

Set the factor '(100 + -1x)' equal to zero and attempt to solve: Simplifying 100 + -1x = 0 Solving 100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1x = 0 + -100 -1x = 0 + -100 Combine like terms: 0 + -100 = -100 -1x = -100 Divide each side by '-1'. x = 100 Simplifying x = 100

Subproblem 2

Set the factor '(200 + -1x)' equal to zero and attempt to solve: Simplifying 200 + -1x = 0 Solving 200 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + -1x = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -1x = 0 + -200 -1x = 0 + -200 Combine like terms: 0 + -200 = -200 -1x = -200 Divide each side by '-1'. x = 200 Simplifying x = 200

Solution

x = {100, 200}

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