190x^2+1009x=x+10987214

Solution for 190x^2+1009x=x+10987214 equation:

Simplifying
190x2 + 1009x = x + 10987214

Reorder the terms:
1009x + 190x2 = x + 10987214

Reorder the terms:
1009x + 190x2 = 10987214 + x

Solving
1009x + 190x2 = 10987214 + x

Solving for variable 'x'.

Reorder the terms:
-10987214 + 1009x + -1x + 190x2 = 10987214 + x + -10987214 + -1x

Combine like terms: 1009x + -1x = 1008x
-10987214 + 1008x + 190x2 = 10987214 + x + -10987214 + -1x

Reorder the terms:
-10987214 + 1008x + 190x2 = 10987214 + -10987214 + x + -1x

Combine like terms: 10987214 + -10987214 = 0
-10987214 + 1008x + 190x2 = 0 + x + -1x
-10987214 + 1008x + 190x2 = x + -1x

Combine like terms: x + -1x = 0
-10987214 + 1008x + 190x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5493607 + 504x + 95x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5493607 + 504x + 95x2)' equal to zero and attempt to solve:

Simplifying
-5493607 + 504x + 95x2 = 0

Solving
-5493607 + 504x + 95x2 = 0

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

Divide each side by '95'.
-57827.44211 + 5.305263158x + x2 = 0

Move the constant term to the right:

Add '57827.44211' to each side of the equation.
-57827.44211 + 5.305263158x + 57827.44211 + x2 = 0 + 57827.44211

Reorder the terms:
-57827.44211 + 57827.44211 + 5.305263158x + x2 = 0 + 57827.44211

Combine like terms: -57827.44211 + 57827.44211 = 0.00000
0.00000 + 5.305263158x + x2 = 0 + 57827.44211
5.305263158x + x2 = 0 + 57827.44211

Combine like terms: 0 + 57827.44211 = 57827.44211
5.305263158x + x2 = 57827.44211

The x term is 5.305263158x.  Take half its coefficient (2.652631579).
Square it (7.036454294) and add it to both sides.

Add '7.036454294' to each side of the equation.
5.305263158x + 7.036454294 + x2 = 57827.44211 + 7.036454294

Reorder the terms:
7.036454294 + 5.305263158x + x2 = 57827.44211 + 7.036454294

Combine like terms: 57827.44211 + 7.036454294 = 57834.478564294
7.036454294 + 5.305263158x + x2 = 57834.478564294

Factor a perfect square on the left side:
(x + 2.652631579)(x + 2.652631579) = 57834.478564294

Calculate the square root of the right side: 240.488000874

Break this problem into two subproblems by setting 
(x + 2.652631579) equal to 240.488000874 and -240.488000874.

Subproblem 1
x + 2.652631579 = 240.488000874

Simplifying
x + 2.652631579 = 240.488000874

Reorder the terms:
2.652631579 + x = 240.488000874

Solving
2.652631579 + x = 240.488000874

Solving for variable 'x'.

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

Add '-2.652631579' to each side of the equation.
2.652631579 + -2.652631579 + x = 240.488000874 + -2.652631579

Combine like terms: 2.652631579 + -2.652631579 = 0.000000000
0.000000000 + x = 240.488000874 + -2.652631579
x = 240.488000874 + -2.652631579

Combine like terms: 240.488000874 + -2.652631579 = 237.835369295
x = 237.835369295

Simplifying
x = 237.835369295

Subproblem 2
x + 2.652631579 = -240.488000874

Simplifying
x + 2.652631579 = -240.488000874

Reorder the terms:
2.652631579 + x = -240.488000874

Solving
2.652631579 + x = -240.488000874

Solving for variable 'x'.

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

Add '-2.652631579' to each side of the equation.
2.652631579 + -2.652631579 + x = -240.488000874 + -2.652631579

Combine like terms: 2.652631579 + -2.652631579 = 0.000000000
0.000000000 + x = -240.488000874 + -2.652631579
x = -240.488000874 + -2.652631579

Combine like terms: -240.488000874 + -2.652631579 = -243.140632453
x = -243.140632453

Simplifying
x = -243.140632453

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {237.835369295, -243.140632453}
Solution
x = {237.835369295, -243.140632453}