72=(17+x)x

Solution for 72=(17+x)x equation:

Simplifying
72 = (17 + x) * x

Reorder the terms for easier multiplication:
72 = x(17 + x)
72 = (17 * x + x * x)
72 = (17x + x2)

Solving
72 = 17x + x2

Solving for variable 'x'.

Reorder the terms:
72 + -17x + -1x2 = 17x + -17x + x2 + -1x2

Combine like terms: 17x + -17x = 0
72 + -17x + -1x2 = 0 + x2 + -1x2
72 + -17x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
72 + -17x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-72 + 17x + x2 = 0

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 17x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 17x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 17x + x2 = 0 + 72
17x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
17x + x2 = 72

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 72 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 72 + 72.25

Combine like terms: 72 + 72.25 = 144.25
72.25 + 17x + x2 = 144.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 144.25

Calculate the square root of the right side: 12.010412149

Break this problem into two subproblems by setting 
(x + 8.5) equal to 12.010412149 and -12.010412149.

Subproblem 1
x + 8.5 = 12.010412149

Simplifying
x + 8.5 = 12.010412149

Reorder the terms:
8.5 + x = 12.010412149

Solving
8.5 + x = 12.010412149

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 12.010412149 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 12.010412149 + -8.5
x = 12.010412149 + -8.5

Combine like terms: 12.010412149 + -8.5 = 3.510412149
x = 3.510412149

Simplifying
x = 3.510412149

Subproblem 2
x + 8.5 = -12.010412149

Simplifying
x + 8.5 = -12.010412149

Reorder the terms:
8.5 + x = -12.010412149

Solving
8.5 + x = -12.010412149

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -12.010412149 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -12.010412149 + -8.5
x = -12.010412149 + -8.5

Combine like terms: -12.010412149 + -8.5 = -20.510412149
x = -20.510412149

Simplifying
x = -20.510412149

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.510412149, -20.510412149}