6x^2+33x+13=0

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Solution for 6x^2+33x+13=0 equation: 


Simplifying
6x2 + 33x + 13 = 0

Reorder the terms:
13 + 33x + 6x2 = 0

Solving
13 + 33x + 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'.
2.166666667 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-2.166666667' to each side of the equation.
2.166666667 + 5.5x + -2.166666667 + x2 = 0 + -2.166666667

Reorder the terms:
2.166666667 + -2.166666667 + 5.5x + x2 = 0 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + 5.5x + x2 = 0 + -2.166666667
5.5x + x2 = 0 + -2.166666667

Combine like terms: 0 + -2.166666667 = -2.166666667
5.5x + x2 = -2.166666667

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -2.166666667 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -2.166666667 + 7.5625

Combine like terms: -2.166666667 + 7.5625 = 5.395833333
7.5625 + 5.5x + x2 = 5.395833333

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 5.395833333

Calculate the square root of the right side: 2.322893311

Break this problem into two subproblems by setting 
(x + 2.75) equal to 2.322893311 and -2.322893311.


Subproblem 1
x + 2.75 = 2.322893311

Simplifying
x + 2.75 = 2.322893311

Reorder the terms:
2.75 + x = 2.322893311

Solving
2.75 + x = 2.322893311

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = 2.322893311 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = 2.322893311 + -2.75
x = 2.322893311 + -2.75

Combine like terms: 2.322893311 + -2.75 = -0.427106689
x = -0.427106689

Simplifying
x = -0.427106689


Subproblem 2
x + 2.75 = -2.322893311

Simplifying
x + 2.75 = -2.322893311

Reorder the terms:
2.75 + x = -2.322893311

Solving
2.75 + x = -2.322893311

Solving for variable 'x'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + x = -2.322893311 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + x = -2.322893311 + -2.75
x = -2.322893311 + -2.75

Combine like terms: -2.322893311 + -2.75 = -5.072893311
x = -5.072893311

Simplifying
x = -5.072893311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.427106689, -5.072893311}

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