6x^2+4x=29

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Solution for 6x^2+4x=29 equation: 


Simplifying
6x2 + 4x = 29

Reorder the terms:
4x + 6x2 = 29

Solving
4x + 6x2 = 29

Solving for variable 'x'.

Reorder the terms:
-29 + 4x + 6x2 = 29 + -29

Combine like terms: 29 + -29 = 0
-29 + 4x + 6x2 = 0

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

Divide each side by '6'.
-4.833333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '4.833333333' to each side of the equation.
-4.833333333 + 0.6666666667x + 4.833333333 + x2 = 0 + 4.833333333

Reorder the terms:
-4.833333333 + 4.833333333 + 0.6666666667x + x2 = 0 + 4.833333333

Combine like terms: -4.833333333 + 4.833333333 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 4.833333333
0.6666666667x + x2 = 0 + 4.833333333

Combine like terms: 0 + 4.833333333 = 4.833333333
0.6666666667x + x2 = 4.833333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 4.833333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 4.833333333 + 0.1111111112

Combine like terms: 4.833333333 + 0.1111111112 = 4.9444444442
0.1111111112 + 0.6666666667x + x2 = 4.9444444442

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 4.9444444442

Calculate the square root of the right side: 2.223610677

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 2.223610677 and -2.223610677.


Subproblem 1
x + 0.3333333334 = 2.223610677

Simplifying
x + 0.3333333334 = 2.223610677

Reorder the terms:
0.3333333334 + x = 2.223610677

Solving
0.3333333334 + x = 2.223610677

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 2.223610677 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 2.223610677 + -0.3333333334
x = 2.223610677 + -0.3333333334

Combine like terms: 2.223610677 + -0.3333333334 = 1.8902773436
x = 1.8902773436

Simplifying
x = 1.8902773436


Subproblem 2
x + 0.3333333334 = -2.223610677

Simplifying
x + 0.3333333334 = -2.223610677

Reorder the terms:
0.3333333334 + x = -2.223610677

Solving
0.3333333334 + x = -2.223610677

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -2.223610677 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -2.223610677 + -0.3333333334
x = -2.223610677 + -0.3333333334

Combine like terms: -2.223610677 + -0.3333333334 = -2.5569440104
x = -2.5569440104

Simplifying
x = -2.5569440104


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8902773436, -2.5569440104}

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