-6x^2+26x+28=0

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Solution for -6x^2+26x+28=0 equation: 


Simplifying
-6x2 + 26x + 28 = 0

Reorder the terms:
28 + 26x + -6x2 = 0

Solving
28 + 26x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 13x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + 13x + -3x2)' equal to zero and attempt to solve:

Simplifying
14 + 13x + -3x2 = 0

Solving
14 + 13x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-4.666666667 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -4.333333333x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -4.333333333x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -4.333333333x + x2 = 0 + 4.666666667
-4.333333333x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-4.333333333x + x2 = 4.666666667

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 = 4.666666667 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 4.666666667 + 4.694444446

Combine like terms: 4.666666667 + 4.694444446 = 9.361111113
4.694444446 + -4.333333333x + x2 = 9.361111113

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 9.361111113

Calculate the square root of the right side: 3.059593292

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 3.059593292 and -3.059593292.


Subproblem 1
x + -2.166666667 = 3.059593292

Simplifying
x + -2.166666667 = 3.059593292

Reorder the terms:
-2.166666667 + x = 3.059593292

Solving
-2.166666667 + x = 3.059593292

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 = 3.059593292 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 3.059593292 + 2.166666667
x = 3.059593292 + 2.166666667

Combine like terms: 3.059593292 + 2.166666667 = 5.226259959
x = 5.226259959

Simplifying
x = 5.226259959


Subproblem 2
x + -2.166666667 = -3.059593292

Simplifying
x + -2.166666667 = -3.059593292

Reorder the terms:
-2.166666667 + x = -3.059593292

Solving
-2.166666667 + x = -3.059593292

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 = -3.059593292 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -3.059593292 + 2.166666667
x = -3.059593292 + 2.166666667

Combine like terms: -3.059593292 + 2.166666667 = -0.892926625
x = -0.892926625

Simplifying
x = -0.892926625


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.226259959, -0.892926625}
Solution
x = {5.226259959, -0.892926625}

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