6x^2+x+9*4x+2=

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Solution for 6x^2+x+9*4x+2= equation: 


Simplifying
6x2 + x + 9 * 4x + 2 = 0

Multiply 9 * 4
6x2 + x + 36x + 2 = 0

Reorder the terms:
2 + x + 36x + 6x2 = 0

Combine like terms: x + 36x = 37x
2 + 37x + 6x2 = 0

Solving
2 + 37x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
0.3333333333 + 6.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 6.166666667x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 6.166666667x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 6.166666667x + x2 = 0 + -0.3333333333
6.166666667x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
6.166666667x + x2 = -0.3333333333

The x term is 6.166666667x.  Take half its coefficient (3.083333334).
Square it (9.506944449) and add it to both sides.

Add '9.506944449' to each side of the equation.
6.166666667x + 9.506944449 + x2 = -0.3333333333 + 9.506944449

Reorder the terms:
9.506944449 + 6.166666667x + x2 = -0.3333333333 + 9.506944449

Combine like terms: -0.3333333333 + 9.506944449 = 9.1736111157
9.506944449 + 6.166666667x + x2 = 9.1736111157

Factor a perfect square on the left side:
(x + 3.083333334)(x + 3.083333334) = 9.1736111157

Calculate the square root of the right side: 3.028796975

Break this problem into two subproblems by setting 
(x + 3.083333334) equal to 3.028796975 and -3.028796975.


Subproblem 1
x + 3.083333334 = 3.028796975

Simplifying
x + 3.083333334 = 3.028796975

Reorder the terms:
3.083333334 + x = 3.028796975

Solving
3.083333334 + x = 3.028796975

Solving for variable 'x'.

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

Add '-3.083333334' to each side of the equation.
3.083333334 + -3.083333334 + x = 3.028796975 + -3.083333334

Combine like terms: 3.083333334 + -3.083333334 = 0.000000000
0.000000000 + x = 3.028796975 + -3.083333334
x = 3.028796975 + -3.083333334

Combine like terms: 3.028796975 + -3.083333334 = -0.054536359
x = -0.054536359

Simplifying
x = -0.054536359


Subproblem 2
x + 3.083333334 = -3.028796975

Simplifying
x + 3.083333334 = -3.028796975

Reorder the terms:
3.083333334 + x = -3.028796975

Solving
3.083333334 + x = -3.028796975

Solving for variable 'x'.

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

Add '-3.083333334' to each side of the equation.
3.083333334 + -3.083333334 + x = -3.028796975 + -3.083333334

Combine like terms: 3.083333334 + -3.083333334 = 0.000000000
0.000000000 + x = -3.028796975 + -3.083333334
x = -3.028796975 + -3.083333334

Combine like terms: -3.028796975 + -3.083333334 = -6.112130309
x = -6.112130309

Simplifying
x = -6.112130309


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.054536359, -6.112130309}

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