8x(x+25)=600

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Solution for 8x(x+25)=600 equation: 


Simplifying
8x(x + 25) = 600

Reorder the terms:
8x(25 + x) = 600
(25 * 8x + x * 8x) = 600
(200x + 8x2) = 600

Solving
200x + 8x2 = 600

Solving for variable 'x'.

Reorder the terms:
-600 + 200x + 8x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-600 + 200x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-75 + 25x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-75 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
-75 + 25x + x2 = 0

Solving
-75 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 25x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 25x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 25x + x2 = 0 + 75
25x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
25x + x2 = 75

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 = 75 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 75 + 156.25

Combine like terms: 75 + 156.25 = 231.25
156.25 + 25x + x2 = 231.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 231.25

Calculate the square root of the right side: 15.206906326

Break this problem into two subproblems by setting 
(x + 12.5) equal to 15.206906326 and -15.206906326.


Subproblem 1
x + 12.5 = 15.206906326

Simplifying
x + 12.5 = 15.206906326

Reorder the terms:
12.5 + x = 15.206906326

Solving
12.5 + x = 15.206906326

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 = 15.206906326 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 15.206906326 + -12.5
x = 15.206906326 + -12.5

Combine like terms: 15.206906326 + -12.5 = 2.706906326
x = 2.706906326

Simplifying
x = 2.706906326


Subproblem 2
x + 12.5 = -15.206906326

Simplifying
x + 12.5 = -15.206906326

Reorder the terms:
12.5 + x = -15.206906326

Solving
12.5 + x = -15.206906326

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 = -15.206906326 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -15.206906326 + -12.5
x = -15.206906326 + -12.5

Combine like terms: -15.206906326 + -12.5 = -27.706906326
x = -27.706906326

Simplifying
x = -27.706906326


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.706906326, -27.706906326}
Solution
x = {2.706906326, -27.706906326}

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