40x(x)+(x+2)=9(x)(x+2)

Solution for 40x(x)+(x+2)=9(x)(x+2) equation:

Simplifying
40x(x) + (x + 2) = 9(x)(x + 2)

Multiply x * x
40x2 + (x + 2) = 9(x)(x + 2)

Reorder the terms:
40x2 + (2 + x) = 9(x)(x + 2)

Remove parenthesis around (2 + x)
40x2 + 2 + x = 9(x)(x + 2)

Reorder the terms:
2 + x + 40x2 = 9(x)(x + 2)

Reorder the terms:
2 + x + 40x2 = 9x(2 + x)
2 + x + 40x2 = (2 * 9x + x * 9x)
2 + x + 40x2 = (18x + 9x2)

Solving
2 + x + 40x2 = 18x + 9x2

Solving for variable 'x'.

Reorder the terms:
2 + x + -18x + 40x2 + -9x2 = 18x + 9x2 + -18x + -9x2

Combine like terms: x + -18x = -17x
2 + -17x + 40x2 + -9x2 = 18x + 9x2 + -18x + -9x2

Combine like terms: 40x2 + -9x2 = 31x2
2 + -17x + 31x2 = 18x + 9x2 + -18x + -9x2

Reorder the terms:
2 + -17x + 31x2 = 18x + -18x + 9x2 + -9x2

Combine like terms: 18x + -18x = 0
2 + -17x + 31x2 = 0 + 9x2 + -9x2
2 + -17x + 31x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
2 + -17x + 31x2 = 0

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

Divide each side by '31'.
0.06451612903 + -0.5483870968x + x2 = 0

Move the constant term to the right:

Add '-0.06451612903' to each side of the equation.
0.06451612903 + -0.5483870968x + -0.06451612903 + x2 = 0 + -0.06451612903

Reorder the terms:
0.06451612903 + -0.06451612903 + -0.5483870968x + x2 = 0 + -0.06451612903

Combine like terms: 0.06451612903 + -0.06451612903 = 0.00000000000
0.00000000000 + -0.5483870968x + x2 = 0 + -0.06451612903
-0.5483870968x + x2 = 0 + -0.06451612903

Combine like terms: 0 + -0.06451612903 = -0.06451612903
-0.5483870968x + x2 = -0.06451612903

The x term is -0.5483870968x.  Take half its coefficient (-0.2741935484).
Square it (0.07518210198) and add it to both sides.

Add '0.07518210198' to each side of the equation.
-0.5483870968x + 0.07518210198 + x2 = -0.06451612903 + 0.07518210198

Reorder the terms:
0.07518210198 + -0.5483870968x + x2 = -0.06451612903 + 0.07518210198

Combine like terms: -0.06451612903 + 0.07518210198 = 0.01066597295
0.07518210198 + -0.5483870968x + x2 = 0.01066597295

Factor a perfect square on the left side:
(x + -0.2741935484)(x + -0.2741935484) = 0.01066597295

Calculate the square root of the right side: 0.103276197

Break this problem into two subproblems by setting 
(x + -0.2741935484) equal to 0.103276197 and -0.103276197.

Subproblem 1
x + -0.2741935484 = 0.103276197

Simplifying
x + -0.2741935484 = 0.103276197

Reorder the terms:
-0.2741935484 + x = 0.103276197

Solving
-0.2741935484 + x = 0.103276197

Solving for variable 'x'.

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

Add '0.2741935484' to each side of the equation.
-0.2741935484 + 0.2741935484 + x = 0.103276197 + 0.2741935484

Combine like terms: -0.2741935484 + 0.2741935484 = 0.0000000000
0.0000000000 + x = 0.103276197 + 0.2741935484
x = 0.103276197 + 0.2741935484

Combine like terms: 0.103276197 + 0.2741935484 = 0.3774697454
x = 0.3774697454

Simplifying
x = 0.3774697454

Subproblem 2
x + -0.2741935484 = -0.103276197

Simplifying
x + -0.2741935484 = -0.103276197

Reorder the terms:
-0.2741935484 + x = -0.103276197

Solving
-0.2741935484 + x = -0.103276197

Solving for variable 'x'.

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

Add '0.2741935484' to each side of the equation.
-0.2741935484 + 0.2741935484 + x = -0.103276197 + 0.2741935484

Combine like terms: -0.2741935484 + 0.2741935484 = 0.0000000000
0.0000000000 + x = -0.103276197 + 0.2741935484
x = -0.103276197 + 0.2741935484

Combine like terms: -0.103276197 + 0.2741935484 = 0.1709173514
x = 0.1709173514

Simplifying
x = 0.1709173514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3774697454, 0.1709173514}