x(200-x)=7500

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Solution for x(200-x)=7500 equation:


Simplifying
x(200 + -1x) = 7500
(200 * x + -1x * x) = 7500
(200x + -1x2) = 7500

Solving
200x + -1x2 = 7500

Solving for variable 'x'.

Reorder the terms:
-7500 + 200x + -1x2 = 7500 + -7500

Combine like terms: 7500 + -7500 = 0
-7500 + 200x + -1x2 = 0

Factor a trinomial.
(-150 + x)(50 + -1x) = 0

Subproblem 1

Set the factor '(-150 + x)' equal to zero and attempt to solve: Simplifying -150 + x = 0 Solving -150 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 0 + 150 Combine like terms: -150 + 150 = 0 0 + x = 0 + 150 x = 0 + 150 Combine like terms: 0 + 150 = 150 x = 150 Simplifying x = 150

Subproblem 2

Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50

Solution

x = {150, 50}

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