72=x(2x+7)+(10x-1)

Solution for 72=x(2x+7)+(10x-1) equation:

Simplifying
72 = x(2x + 7) + (10x + -1)

Reorder the terms:
72 = x(7 + 2x) + (10x + -1)
72 = (7 * x + 2x * x) + (10x + -1)
72 = (7x + 2x2) + (10x + -1)

Reorder the terms:
72 = 7x + 2x2 + (-1 + 10x)

Remove parenthesis around (-1 + 10x)
72 = 7x + 2x2 + -1 + 10x

Reorder the terms:
72 = -1 + 7x + 10x + 2x2

Combine like terms: 7x + 10x = 17x
72 = -1 + 17x + 2x2

Solving
72 = -1 + 17x + 2x2

Solving for variable 'x'.

Combine like terms: 72 + 1 = 73
73 + -17x + -2x2 = -1 + 17x + 2x2 + 1 + -17x + -2x2

Reorder the terms:
73 + -17x + -2x2 = -1 + 1 + 17x + -17x + 2x2 + -2x2

Combine like terms: -1 + 1 = 0
73 + -17x + -2x2 = 0 + 17x + -17x + 2x2 + -2x2
73 + -17x + -2x2 = 17x + -17x + 2x2 + -2x2

Combine like terms: 17x + -17x = 0
73 + -17x + -2x2 = 0 + 2x2 + -2x2
73 + -17x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
73 + -17x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-36.5 + 8.5x + x2 = 0

Move the constant term to the right:

Add '36.5' to each side of the equation.
-36.5 + 8.5x + 36.5 + x2 = 0 + 36.5

Reorder the terms:
-36.5 + 36.5 + 8.5x + x2 = 0 + 36.5

Combine like terms: -36.5 + 36.5 = 0.0
0.0 + 8.5x + x2 = 0 + 36.5
8.5x + x2 = 0 + 36.5

Combine like terms: 0 + 36.5 = 36.5
8.5x + x2 = 36.5

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 36.5 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 36.5 + 18.0625

Combine like terms: 36.5 + 18.0625 = 54.5625
18.0625 + 8.5x + x2 = 54.5625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 54.5625

Calculate the square root of the right side: 7.386643351

Break this problem into two subproblems by setting 
(x + 4.25) equal to 7.386643351 and -7.386643351.

Subproblem 1
x + 4.25 = 7.386643351

Simplifying
x + 4.25 = 7.386643351

Reorder the terms:
4.25 + x = 7.386643351

Solving
4.25 + x = 7.386643351

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = 7.386643351 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 7.386643351 + -4.25
x = 7.386643351 + -4.25

Combine like terms: 7.386643351 + -4.25 = 3.136643351
x = 3.136643351

Simplifying
x = 3.136643351

Subproblem 2
x + 4.25 = -7.386643351

Simplifying
x + 4.25 = -7.386643351

Reorder the terms:
4.25 + x = -7.386643351

Solving
4.25 + x = -7.386643351

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = -7.386643351 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -7.386643351 + -4.25
x = -7.386643351 + -4.25

Combine like terms: -7.386643351 + -4.25 = -11.636643351
x = -11.636643351

Simplifying
x = -11.636643351

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.136643351, -11.636643351}