6x^2+26x-9=0

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Solution for 6x^2+26x-9=0 equation: 


Simplifying
6x2 + 26x + -9 = 0

Reorder the terms:
-9 + 26x + 6x2 = 0

Solving
-9 + 26x + 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'.
-1.5 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 4.333333333x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 4.333333333x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 4.333333333x + x2 = 0 + 1.5
4.333333333x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
4.333333333x + x2 = 1.5

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 1.5 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 1.5 + 4.694444446

Combine like terms: 1.5 + 4.694444446 = 6.194444446
4.694444446 + 4.333333333x + x2 = 6.194444446

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 6.194444446

Calculate the square root of the right side: 2.488864087

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 2.488864087 and -2.488864087.


Subproblem 1
x + 2.166666667 = 2.488864087

Simplifying
x + 2.166666667 = 2.488864087

Reorder the terms:
2.166666667 + x = 2.488864087

Solving
2.166666667 + x = 2.488864087

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 2.488864087 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 2.488864087 + -2.166666667
x = 2.488864087 + -2.166666667

Combine like terms: 2.488864087 + -2.166666667 = 0.32219742
x = 0.32219742

Simplifying
x = 0.32219742


Subproblem 2
x + 2.166666667 = -2.488864087

Simplifying
x + 2.166666667 = -2.488864087

Reorder the terms:
2.166666667 + x = -2.488864087

Solving
2.166666667 + x = -2.488864087

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -2.488864087 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -2.488864087 + -2.166666667
x = -2.488864087 + -2.166666667

Combine like terms: -2.488864087 + -2.166666667 = -4.655530754
x = -4.655530754

Simplifying
x = -4.655530754


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.32219742, -4.655530754}

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