425=25x(10x+250)

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Solution for 425=25x(10x+250) equation: 


Simplifying
425 = 25x(10x + 250)

Reorder the terms:
425 = 25x(250 + 10x)
425 = (250 * 25x + 10x * 25x)
425 = (6250x + 250x2)

Solving
425 = 6250x + 250x2

Solving for variable 'x'.

Reorder the terms:
425 + -6250x + -250x2 = 6250x + -6250x + 250x2 + -250x2

Combine like terms: 6250x + -6250x = 0
425 + -6250x + -250x2 = 0 + 250x2 + -250x2
425 + -6250x + -250x2 = 250x2 + -250x2

Combine like terms: 250x2 + -250x2 = 0
425 + -6250x + -250x2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(17 + -250x + -10x2) = 0

Ignore the factor 25.

Subproblem 1
Set the factor '(17 + -250x + -10x2)' equal to zero and attempt to solve:

Simplifying
17 + -250x + -10x2 = 0

Solving
17 + -250x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-1.7 + 25x + x2 = 0.0

Move the constant term to the right:

Add '1.7' to each side of the equation.
-1.7 + 25x + 1.7 + x2 = 0.0 + 1.7

Reorder the terms:
-1.7 + 1.7 + 25x + x2 = 0.0 + 1.7

Combine like terms: -1.7 + 1.7 = 0.0
0.0 + 25x + x2 = 0.0 + 1.7
25x + x2 = 0.0 + 1.7

Combine like terms: 0.0 + 1.7 = 1.7
25x + x2 = 1.7

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 1.7 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 1.7 + 156.25

Combine like terms: 1.7 + 156.25 = 157.95
156.25 + 25x + x2 = 157.95

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 157.95

Calculate the square root of the right side: 12.567816039

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.567816039 and -12.567816039.


Subproblem 1
x + 12.5 = 12.567816039

Simplifying
x + 12.5 = 12.567816039

Reorder the terms:
12.5 + x = 12.567816039

Solving
12.5 + x = 12.567816039

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 12.567816039 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 12.567816039 + -12.5
x = 12.567816039 + -12.5

Combine like terms: 12.567816039 + -12.5 = 0.067816039
x = 0.067816039

Simplifying
x = 0.067816039


Subproblem 2
x + 12.5 = -12.567816039

Simplifying
x + 12.5 = -12.567816039

Reorder the terms:
12.5 + x = -12.567816039

Solving
12.5 + x = -12.567816039

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -12.567816039 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -12.567816039 + -12.5
x = -12.567816039 + -12.5

Combine like terms: -12.567816039 + -12.5 = -25.067816039
x = -25.067816039

Simplifying
x = -25.067816039


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.067816039, -25.067816039}
Solution
x = {0.067816039, -25.067816039}

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