0=50+5x-x^2

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Solution for 0=50+5x-x^2 equation:


Simplifying
0 = 50 + 5x + -1x2

Solving
0 = 50 + 5x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -50 = -50
-50 + -5x + x2 = 50 + 5x + -1x2 + -50 + -5x + x2

Reorder the terms:
-50 + -5x + x2 = 50 + -50 + 5x + -5x + -1x2 + x2

Combine like terms: 50 + -50 = 0
-50 + -5x + x2 = 0 + 5x + -5x + -1x2 + x2
-50 + -5x + x2 = 5x + -5x + -1x2 + x2

Combine like terms: 5x + -5x = 0
-50 + -5x + x2 = 0 + -1x2 + x2
-50 + -5x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-50 + -5x + x2 = 0

Factor a trinomial.
(-5 + -1x)(10 + -1x) = 0

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {-5, 10}

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