8x+72+9x=2x^2+18x

Solution for 8x+72+9x=2x^2+18x equation:

Simplifying
8x + 72 + 9x = 2x2 + 18x

Reorder the terms:
72 + 8x + 9x = 2x2 + 18x

Combine like terms: 8x + 9x = 17x
72 + 17x = 2x2 + 18x

Reorder the terms:
72 + 17x = 18x + 2x2

Solving
72 + 17x = 18x + 2x2

Solving for variable 'x'.

Combine like terms: 17x + -18x = -1x
72 + -1x + -2x2 = 18x + 2x2 + -18x + -2x2

Reorder the terms:
72 + -1x + -2x2 = 18x + -18x + 2x2 + -2x2

Combine like terms: 18x + -18x = 0
72 + -1x + -2x2 = 0 + 2x2 + -2x2
72 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
72 + -1x + -2x2 = 0

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

Divide each side by '-2'.
-36 + 0.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 0.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 0.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 0.5x + x2 = 0 + 36
0.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
0.5x + x2 = 36

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 36 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 36 + 0.0625

Combine like terms: 36 + 0.0625 = 36.0625
0.0625 + 0.5x + x2 = 36.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 36.0625

Calculate the square root of the right side: 6.005206075

Break this problem into two subproblems by setting 
(x + 0.25) equal to 6.005206075 and -6.005206075.

Subproblem 1
x + 0.25 = 6.005206075

Simplifying
x + 0.25 = 6.005206075

Reorder the terms:
0.25 + x = 6.005206075

Solving
0.25 + x = 6.005206075

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 6.005206075 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 6.005206075 + -0.25
x = 6.005206075 + -0.25

Combine like terms: 6.005206075 + -0.25 = 5.755206075
x = 5.755206075

Simplifying
x = 5.755206075

Subproblem 2
x + 0.25 = -6.005206075

Simplifying
x + 0.25 = -6.005206075

Reorder the terms:
0.25 + x = -6.005206075

Solving
0.25 + x = -6.005206075

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -6.005206075 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -6.005206075 + -0.25
x = -6.005206075 + -0.25

Combine like terms: -6.005206075 + -0.25 = -6.255206075
x = -6.255206075

Simplifying
x = -6.255206075

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.755206075, -6.255206075}