250x-2x^2=5000

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Solution for 250x-2x^2=5000 equation:


Simplifying
250x + -2x2 = 5000

Solving
250x + -2x2 = 5000

Solving for variable 'x'.

Reorder the terms:
-5000 + 250x + -2x2 = 5000 + -5000

Combine like terms: 5000 + -5000 = 0
-5000 + 250x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2500 + 125x + -1x2) = 0

Factor a trinomial.
2((-100 + x)(25 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-100 + x)' equal to zero and attempt to solve: Simplifying -100 + x = 0 Solving -100 + x = 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 + x = 0 + 100 Combine like terms: -100 + 100 = 0 0 + x = 0 + 100 x = 0 + 100 Combine like terms: 0 + 100 = 100 x = 100 Simplifying x = 100

Subproblem 2

Set the factor '(25 + -1x)' equal to zero and attempt to solve: Simplifying 25 + -1x = 0 Solving 25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1x = 0 + -25 -1x = 0 + -25 Combine like terms: 0 + -25 = -25 -1x = -25 Divide each side by '-1'. x = 25 Simplifying x = 25

Solution

x = {100, 25}

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