4x+2x*9x=2470

Solution for 4x+2x*9x=2470 equation:

Simplifying
4x + 2x * 9x = 2470

Reorder the terms for easier multiplication:
4x + 2 * 9x * x = 2470

Multiply 2 * 9
4x + 18x * x = 2470

Multiply x * x
4x + 18x2 = 2470

Solving
4x + 18x2 = 2470

Solving for variable 'x'.

Reorder the terms:
-2470 + 4x + 18x2 = 2470 + -2470

Combine like terms: 2470 + -2470 = 0
-2470 + 4x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1235 + 2x + 9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1235 + 2x + 9x2)' equal to zero and attempt to solve:

Simplifying
-1235 + 2x + 9x2 = 0

Solving
-1235 + 2x + 9x2 = 0

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

Divide each side by '9'.
-137.2222222 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '137.2222222' to each side of the equation.
-137.2222222 + 0.2222222222x + 137.2222222 + x2 = 0 + 137.2222222

Reorder the terms:
-137.2222222 + 137.2222222 + 0.2222222222x + x2 = 0 + 137.2222222

Combine like terms: -137.2222222 + 137.2222222 = 0.0000000
0.0000000 + 0.2222222222x + x2 = 0 + 137.2222222
0.2222222222x + x2 = 0 + 137.2222222

Combine like terms: 0 + 137.2222222 = 137.2222222
0.2222222222x + x2 = 137.2222222

The x term is 0.2222222222x.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222x + 0.01234567901 + x2 = 137.2222222 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 137.2222222 + 0.01234567901

Combine like terms: 137.2222222 + 0.01234567901 = 137.23456787901
0.01234567901 + 0.2222222222x + x2 = 137.23456787901

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 137.23456787901

Calculate the square root of the right side: 11.714715868

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 11.714715868 and -11.714715868.

Subproblem 1
x + 0.1111111111 = 11.714715868

Simplifying
x + 0.1111111111 = 11.714715868

Reorder the terms:
0.1111111111 + x = 11.714715868

Solving
0.1111111111 + x = 11.714715868

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = 11.714715868 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = 11.714715868 + -0.1111111111
x = 11.714715868 + -0.1111111111

Combine like terms: 11.714715868 + -0.1111111111 = 11.6036047569
x = 11.6036047569

Simplifying
x = 11.6036047569

Subproblem 2
x + 0.1111111111 = -11.714715868

Simplifying
x + 0.1111111111 = -11.714715868

Reorder the terms:
0.1111111111 + x = -11.714715868

Solving
0.1111111111 + x = -11.714715868

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x = -11.714715868 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x = -11.714715868 + -0.1111111111
x = -11.714715868 + -0.1111111111

Combine like terms: -11.714715868 + -0.1111111111 = -11.8258269791
x = -11.8258269791

Simplifying
x = -11.8258269791

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.6036047569, -11.8258269791}
Solution
x = {11.6036047569, -11.8258269791}