6x^2-14x-28=0

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Solution for 6x^2-14x-28=0 equation: 


Simplifying
6x2 + -14x + -28 = 0

Reorder the terms:
-28 + -14x + 6x2 = 0

Solving
-28 + -14x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -7x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + -7x + 3x2)' equal to zero and attempt to solve:

Simplifying
-14 + -7x + 3x2 = 0

Solving
-14 + -7x + 3x2 = 0

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

Divide each side by '3'.
-4.666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -2.333333333x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -2.333333333x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + 4.666666667
-2.333333333x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-2.333333333x + x2 = 4.666666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 4.666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 4.666666667 + 1.361111112

Combine like terms: 4.666666667 + 1.361111112 = 6.027777779
1.361111112 + -2.333333333x + x2 = 6.027777779

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 6.027777779

Calculate the square root of the right side: 2.455153311

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 2.455153311 and -2.455153311.


Subproblem 1
x + -1.166666667 = 2.455153311

Simplifying
x + -1.166666667 = 2.455153311

Reorder the terms:
-1.166666667 + x = 2.455153311

Solving
-1.166666667 + x = 2.455153311

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 2.455153311 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 2.455153311 + 1.166666667
x = 2.455153311 + 1.166666667

Combine like terms: 2.455153311 + 1.166666667 = 3.621819978
x = 3.621819978

Simplifying
x = 3.621819978


Subproblem 2
x + -1.166666667 = -2.455153311

Simplifying
x + -1.166666667 = -2.455153311

Reorder the terms:
-1.166666667 + x = -2.455153311

Solving
-1.166666667 + x = -2.455153311

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -2.455153311 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -2.455153311 + 1.166666667
x = -2.455153311 + 1.166666667

Combine like terms: -2.455153311 + 1.166666667 = -1.288486644
x = -1.288486644

Simplifying
x = -1.288486644


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.621819978, -1.288486644}
Solution
x = {3.621819978, -1.288486644}

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