6x^2+46x-28=0

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Solution for 6x^2+46x-28=0 equation: 


Simplifying
6x2 + 46x + -28 = 0

Reorder the terms:
-28 + 46x + 6x2 = 0

Solving
-28 + 46x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 23x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + 23x + 3x2)' equal to zero and attempt to solve:

Simplifying
-14 + 23x + 3x2 = 0

Solving
-14 + 23x + 3x2 = 0

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

Divide each side by '3'.
-4.666666667 + 7.666666667x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 7.666666667x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 7.666666667x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 7.666666667x + x2 = 0 + 4.666666667
7.666666667x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
7.666666667x + x2 = 4.666666667

The x term is 7.666666667x.  Take half its coefficient (3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
7.666666667x + 14.69444445 + x2 = 4.666666667 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667x + x2 = 4.666666667 + 14.69444445

Combine like terms: 4.666666667 + 14.69444445 = 19.361111117
14.69444445 + 7.666666667x + x2 = 19.361111117

Factor a perfect square on the left side:
(x + 3.833333334)(x + 3.833333334) = 19.361111117

Calculate the square root of the right side: 4.400126261

Break this problem into two subproblems by setting 
(x + 3.833333334) equal to 4.400126261 and -4.400126261.


Subproblem 1
x + 3.833333334 = 4.400126261

Simplifying
x + 3.833333334 = 4.400126261

Reorder the terms:
3.833333334 + x = 4.400126261

Solving
3.833333334 + x = 4.400126261

Solving for variable 'x'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + x = 4.400126261 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + x = 4.400126261 + -3.833333334
x = 4.400126261 + -3.833333334

Combine like terms: 4.400126261 + -3.833333334 = 0.566792927
x = 0.566792927

Simplifying
x = 0.566792927


Subproblem 2
x + 3.833333334 = -4.400126261

Simplifying
x + 3.833333334 = -4.400126261

Reorder the terms:
3.833333334 + x = -4.400126261

Solving
3.833333334 + x = -4.400126261

Solving for variable 'x'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + x = -4.400126261 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + x = -4.400126261 + -3.833333334
x = -4.400126261 + -3.833333334

Combine like terms: -4.400126261 + -3.833333334 = -8.233459595
x = -8.233459595

Simplifying
x = -8.233459595


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.566792927, -8.233459595}
Solution
x = {0.566792927, -8.233459595}

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