8x(5x-200)=1414

Solution for 8x(5x-200)=1414 equation:

Simplifying
8x(5x + -200) = 1414

Reorder the terms:
8x(-200 + 5x) = 1414
(-200 * 8x + 5x * 8x) = 1414
(-1600x + 40x2) = 1414

Solving
-1600x + 40x2 = 1414

Solving for variable 'x'.

Reorder the terms:
-1414 + -1600x + 40x2 = 1414 + -1414

Combine like terms: 1414 + -1414 = 0
-1414 + -1600x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-707 + -800x + 20x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-707 + -800x + 20x2)' equal to zero and attempt to solve:

Simplifying
-707 + -800x + 20x2 = 0

Solving
-707 + -800x + 20x2 = 0

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

Divide each side by '20'.
-35.35 + -40x + x2 = 0.0

Move the constant term to the right:

Add '35.35' to each side of the equation.
-35.35 + -40x + 35.35 + x2 = 0.0 + 35.35

Reorder the terms:
-35.35 + 35.35 + -40x + x2 = 0.0 + 35.35

Combine like terms: -35.35 + 35.35 = 0.00
0.00 + -40x + x2 = 0.0 + 35.35
-40x + x2 = 0.0 + 35.35

Combine like terms: 0.0 + 35.35 = 35.35
-40x + x2 = 35.35

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 35.35 + 400

Reorder the terms:
400 + -40x + x2 = 35.35 + 400

Combine like terms: 35.35 + 400 = 435.35
400 + -40x + x2 = 435.35

Factor a perfect square on the left side:
(x + -20)(x + -20) = 435.35

Calculate the square root of the right side: 20.865042535

Break this problem into two subproblems by setting 
(x + -20) equal to 20.865042535 and -20.865042535.

Subproblem 1
x + -20 = 20.865042535

Simplifying
x + -20 = 20.865042535

Reorder the terms:
-20 + x = 20.865042535

Solving
-20 + x = 20.865042535

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 20.865042535 + 20

Combine like terms: -20 + 20 = 0
0 + x = 20.865042535 + 20
x = 20.865042535 + 20

Combine like terms: 20.865042535 + 20 = 40.865042535
x = 40.865042535

Simplifying
x = 40.865042535

Subproblem 2
x + -20 = -20.865042535

Simplifying
x + -20 = -20.865042535

Reorder the terms:
-20 + x = -20.865042535

Solving
-20 + x = -20.865042535

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -20.865042535 + 20

Combine like terms: -20 + 20 = 0
0 + x = -20.865042535 + 20
x = -20.865042535 + 20

Combine like terms: -20.865042535 + 20 = -0.865042535
x = -0.865042535

Simplifying
x = -0.865042535

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {40.865042535, -0.865042535}
Solution
x = {40.865042535, -0.865042535}