200x-x^2=10x+7800

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Solution for 200x-x^2=10x+7800 equation:


Simplifying
200x + -1x2 = 10x + 7800

Reorder the terms:
200x + -1x2 = 7800 + 10x

Solving
200x + -1x2 = 7800 + 10x

Solving for variable 'x'.

Reorder the terms:
-7800 + 200x + -10x + -1x2 = 7800 + 10x + -7800 + -10x

Combine like terms: 200x + -10x = 190x
-7800 + 190x + -1x2 = 7800 + 10x + -7800 + -10x

Reorder the terms:
-7800 + 190x + -1x2 = 7800 + -7800 + 10x + -10x

Combine like terms: 7800 + -7800 = 0
-7800 + 190x + -1x2 = 0 + 10x + -10x
-7800 + 190x + -1x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-7800 + 190x + -1x2 = 0

Factor a trinomial.
(-130 + x)(60 + -1x) = 0

Subproblem 1

Set the factor '(-130 + x)' equal to zero and attempt to solve: Simplifying -130 + x = 0 Solving -130 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '130' to each side of the equation. -130 + 130 + x = 0 + 130 Combine like terms: -130 + 130 = 0 0 + x = 0 + 130 x = 0 + 130 Combine like terms: 0 + 130 = 130 x = 130 Simplifying x = 130

Subproblem 2

Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60

Solution

x = {130, 60}

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