x(25-5x)+358000=5

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Solution for x(25-5x)+358000=5 equation: 


Simplifying
x(25 + -5x) + 358000 = 5
(25 * x + -5x * x) + 358000 = 5
(25x + -5x2) + 358000 = 5

Reorder the terms:
358000 + 25x + -5x2 = 5

Solving
358000 + 25x + -5x2 = 5

Solving for variable 'x'.

Reorder the terms:
358000 + -5 + 25x + -5x2 = 5 + -5

Combine like terms: 358000 + -5 = 357995
357995 + 25x + -5x2 = 5 + -5

Combine like terms: 5 + -5 = 0
357995 + 25x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(71599 + 5x + -1x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(71599 + 5x + -1x2)' equal to zero and attempt to solve:

Simplifying
71599 + 5x + -1x2 = 0

Solving
71599 + 5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-71599 + -5x + x2 = 0

Move the constant term to the right:

Add '71599' to each side of the equation.
-71599 + -5x + 71599 + x2 = 0 + 71599

Reorder the terms:
-71599 + 71599 + -5x + x2 = 0 + 71599

Combine like terms: -71599 + 71599 = 0
0 + -5x + x2 = 0 + 71599
-5x + x2 = 0 + 71599

Combine like terms: 0 + 71599 = 71599
-5x + x2 = 71599

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 71599 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 71599 + 6.25

Combine like terms: 71599 + 6.25 = 71605.25
6.25 + -5x + x2 = 71605.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 71605.25

Calculate the square root of the right side: 267.591573111

Break this problem into two subproblems by setting 
(x + -2.5) equal to 267.591573111 and -267.591573111.


Subproblem 1
x + -2.5 = 267.591573111

Simplifying
x + -2.5 = 267.591573111

Reorder the terms:
-2.5 + x = 267.591573111

Solving
-2.5 + x = 267.591573111

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 267.591573111 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 267.591573111 + 2.5
x = 267.591573111 + 2.5

Combine like terms: 267.591573111 + 2.5 = 270.091573111
x = 270.091573111

Simplifying
x = 270.091573111


Subproblem 2
x + -2.5 = -267.591573111

Simplifying
x + -2.5 = -267.591573111

Reorder the terms:
-2.5 + x = -267.591573111

Solving
-2.5 + x = -267.591573111

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -267.591573111 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -267.591573111 + 2.5
x = -267.591573111 + 2.5

Combine like terms: -267.591573111 + 2.5 = -265.091573111
x = -265.091573111

Simplifying
x = -265.091573111


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {270.091573111, -265.091573111}
Solution
x = {270.091573111, -265.091573111}

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