6x^2-28x=29

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Solution for 6x^2-28x=29 equation: 


Simplifying
6x2 + -28x = 29

Reorder the terms:
-28x + 6x2 = 29

Solving
-28x + 6x2 = 29

Solving for variable 'x'.

Reorder the terms:
-29 + -28x + 6x2 = 29 + -29

Combine like terms: 29 + -29 = 0
-29 + -28x + 6x2 = 0

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

Divide each side by '6'.
-4.833333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '4.833333333' to each side of the equation.
-4.833333333 + -4.666666667x + 4.833333333 + x2 = 0 + 4.833333333

Reorder the terms:
-4.833333333 + 4.833333333 + -4.666666667x + x2 = 0 + 4.833333333

Combine like terms: -4.833333333 + 4.833333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 4.833333333
-4.666666667x + x2 = 0 + 4.833333333

Combine like terms: 0 + 4.833333333 = 4.833333333
-4.666666667x + x2 = 4.833333333

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 4.833333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 4.833333333 + 5.444444448

Combine like terms: 4.833333333 + 5.444444448 = 10.277777781
5.444444448 + -4.666666667x + x2 = 10.277777781

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 10.277777781

Calculate the square root of the right side: 3.205897344

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 3.205897344 and -3.205897344.


Subproblem 1
x + -2.333333334 = 3.205897344

Simplifying
x + -2.333333334 = 3.205897344

Reorder the terms:
-2.333333334 + x = 3.205897344

Solving
-2.333333334 + x = 3.205897344

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 3.205897344 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 3.205897344 + 2.333333334
x = 3.205897344 + 2.333333334

Combine like terms: 3.205897344 + 2.333333334 = 5.539230678
x = 5.539230678

Simplifying
x = 5.539230678


Subproblem 2
x + -2.333333334 = -3.205897344

Simplifying
x + -2.333333334 = -3.205897344

Reorder the terms:
-2.333333334 + x = -3.205897344

Solving
-2.333333334 + x = -3.205897344

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -3.205897344 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -3.205897344 + 2.333333334
x = -3.205897344 + 2.333333334

Combine like terms: -3.205897344 + 2.333333334 = -0.87256401
x = -0.87256401

Simplifying
x = -0.87256401


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.539230678, -0.87256401}

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