x(6x+400)=40000

Solution for x(6x+400)=40000 equation:

Simplifying
x(6x + 400) = 40000

Reorder the terms:
x(400 + 6x) = 40000
(400 * x + 6x * x) = 40000
(400x + 6x2) = 40000

Solving
400x + 6x2 = 40000

Solving for variable 'x'.

Reorder the terms:
-40000 + 400x + 6x2 = 40000 + -40000

Combine like terms: 40000 + -40000 = 0
-40000 + 400x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20000 + 200x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20000 + 200x + 3x2)' equal to zero and attempt to solve:

Simplifying
-20000 + 200x + 3x2 = 0

Solving
-20000 + 200x + 3x2 = 0

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

Divide each side by '3'.
-6666.666667 + 66.66666667x + x2 = 0

Move the constant term to the right:

Add '6666.666667' to each side of the equation.
-6666.666667 + 66.66666667x + 6666.666667 + x2 = 0 + 6666.666667

Reorder the terms:
-6666.666667 + 6666.666667 + 66.66666667x + x2 = 0 + 6666.666667

Combine like terms: -6666.666667 + 6666.666667 = 0.000000
0.000000 + 66.66666667x + x2 = 0 + 6666.666667
66.66666667x + x2 = 0 + 6666.666667

Combine like terms: 0 + 6666.666667 = 6666.666667
66.66666667x + x2 = 6666.666667

The x term is 66.66666667x.  Take half its coefficient (33.33333334).
Square it (1111.111112) and add it to both sides.

Add '1111.111112' to each side of the equation.
66.66666667x + 1111.111112 + x2 = 6666.666667 + 1111.111112

Reorder the terms:
1111.111112 + 66.66666667x + x2 = 6666.666667 + 1111.111112

Combine like terms: 6666.666667 + 1111.111112 = 7777.777779
1111.111112 + 66.66666667x + x2 = 7777.777779

Factor a perfect square on the left side:
(x + 33.33333334)(x + 33.33333334) = 7777.777779

Calculate the square root of the right side: 88.191710376

Break this problem into two subproblems by setting 
(x + 33.33333334) equal to 88.191710376 and -88.191710376.

Subproblem 1
x + 33.33333334 = 88.191710376

Simplifying
x + 33.33333334 = 88.191710376

Reorder the terms:
33.33333334 + x = 88.191710376

Solving
33.33333334 + x = 88.191710376

Solving for variable 'x'.

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

Add '-33.33333334' to each side of the equation.
33.33333334 + -33.33333334 + x = 88.191710376 + -33.33333334

Combine like terms: 33.33333334 + -33.33333334 = 0.00000000
0.00000000 + x = 88.191710376 + -33.33333334
x = 88.191710376 + -33.33333334

Combine like terms: 88.191710376 + -33.33333334 = 54.858377036
x = 54.858377036

Simplifying
x = 54.858377036

Subproblem 2
x + 33.33333334 = -88.191710376

Simplifying
x + 33.33333334 = -88.191710376

Reorder the terms:
33.33333334 + x = -88.191710376

Solving
33.33333334 + x = -88.191710376

Solving for variable 'x'.

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

Add '-33.33333334' to each side of the equation.
33.33333334 + -33.33333334 + x = -88.191710376 + -33.33333334

Combine like terms: 33.33333334 + -33.33333334 = 0.00000000
0.00000000 + x = -88.191710376 + -33.33333334
x = -88.191710376 + -33.33333334

Combine like terms: -88.191710376 + -33.33333334 = -121.525043716
x = -121.525043716

Simplifying
x = -121.525043716

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.858377036, -121.525043716}
Solution
x = {54.858377036, -121.525043716}