224=10x(x+8)

Solution for 224=10x(x+8) equation:

Simplifying
224 = 10x(x + 8)

Reorder the terms:
224 = 10x(8 + x)
224 = (8 * 10x + x * 10x)
224 = (80x + 10x2)

Solving
224 = 80x + 10x2

Solving for variable 'x'.

Reorder the terms:
224 + -80x + -10x2 = 80x + -80x + 10x2 + -10x2

Combine like terms: 80x + -80x = 0
224 + -80x + -10x2 = 0 + 10x2 + -10x2
224 + -80x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
224 + -80x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(112 + -40x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(112 + -40x + -5x2)' equal to zero and attempt to solve:

Simplifying
112 + -40x + -5x2 = 0

Solving
112 + -40x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-22.4 + 8x + x2 = 0

Move the constant term to the right:

Add '22.4' to each side of the equation.
-22.4 + 8x + 22.4 + x2 = 0 + 22.4

Reorder the terms:
-22.4 + 22.4 + 8x + x2 = 0 + 22.4

Combine like terms: -22.4 + 22.4 = 0.0
0.0 + 8x + x2 = 0 + 22.4
8x + x2 = 0 + 22.4

Combine like terms: 0 + 22.4 = 22.4
8x + x2 = 22.4

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 22.4 + 16

Reorder the terms:
16 + 8x + x2 = 22.4 + 16

Combine like terms: 22.4 + 16 = 38.4
16 + 8x + x2 = 38.4

Factor a perfect square on the left side:
(x + 4)(x + 4) = 38.4

Calculate the square root of the right side: 6.196773354

Break this problem into two subproblems by setting 
(x + 4) equal to 6.196773354 and -6.196773354.

Subproblem 1
x + 4 = 6.196773354

Simplifying
x + 4 = 6.196773354

Reorder the terms:
4 + x = 6.196773354

Solving
4 + x = 6.196773354

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 6.196773354 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.196773354 + -4
x = 6.196773354 + -4

Combine like terms: 6.196773354 + -4 = 2.196773354
x = 2.196773354

Simplifying
x = 2.196773354

Subproblem 2
x + 4 = -6.196773354

Simplifying
x + 4 = -6.196773354

Reorder the terms:
4 + x = -6.196773354

Solving
4 + x = -6.196773354

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -6.196773354 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.196773354 + -4
x = -6.196773354 + -4

Combine like terms: -6.196773354 + -4 = -10.196773354
x = -10.196773354

Simplifying
x = -10.196773354

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.196773354, -10.196773354}
Solution
x = {2.196773354, -10.196773354}