0=32x^2-10000x+500000

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Solution for 0=32x^2-10000x+500000 equation: 


Simplifying
0 = 32x2 + -10000x + 500000

Reorder the terms:
0 = 500000 + -10000x + 32x2

Solving
0 = 500000 + -10000x + 32x2

Solving for variable 'x'.

Combine like terms: 0 + -500000 = -500000
-500000 + 10000x + -32x2 = 500000 + -10000x + 32x2 + -500000 + 10000x + -32x2

Reorder the terms:
-500000 + 10000x + -32x2 = 500000 + -500000 + -10000x + 10000x + 32x2 + -32x2

Combine like terms: 500000 + -500000 = 0
-500000 + 10000x + -32x2 = 0 + -10000x + 10000x + 32x2 + -32x2
-500000 + 10000x + -32x2 = -10000x + 10000x + 32x2 + -32x2

Combine like terms: -10000x + 10000x = 0
-500000 + 10000x + -32x2 = 0 + 32x2 + -32x2
-500000 + 10000x + -32x2 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-500000 + 10000x + -32x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-31250 + 625x + -2x2) = 0

Factor a trinomial.
16((-250 + x)(125 + -2x)) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-250 + x)' equal to zero and attempt to solve:

Simplifying
-250 + x = 0

Solving
-250 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '250' to each side of the equation.
-250 + 250 + x = 0 + 250

Combine like terms: -250 + 250 = 0
0 + x = 0 + 250
x = 0 + 250

Combine like terms: 0 + 250 = 250
x = 250

Simplifying
x = 250

Subproblem 2
Set the factor '(125 + -2x)' equal to zero and attempt to solve:

Simplifying
125 + -2x = 0

Solving
125 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-125' to each side of the equation.
125 + -125 + -2x = 0 + -125

Combine like terms: 125 + -125 = 0
0 + -2x = 0 + -125
-2x = 0 + -125

Combine like terms: 0 + -125 = -125
-2x = -125

Divide each side by '-2'.
x = 62.5

Simplifying
x = 62.5
Solution
x = {250, 62.5}

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