6x^2+38x-10=0

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Solution for 6x^2+38x-10=0 equation: 


Simplifying
6x2 + 38x + -10 = 0

Reorder the terms:
-10 + 38x + 6x2 = 0

Solving
-10 + 38x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 19x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 19x + 3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 19x + 3x2 = 0

Solving
-5 + 19x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + 6.333333333x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 6.333333333x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 6.333333333x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 6.333333333x + x2 = 0 + 1.666666667
6.333333333x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
6.333333333x + x2 = 1.666666667

The x term is 6.333333333x.  Take half its coefficient (3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
6.333333333x + 10.02777778 + x2 = 1.666666667 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333x + x2 = 1.666666667 + 10.02777778

Combine like terms: 1.666666667 + 10.02777778 = 11.694444447
10.02777778 + 6.333333333x + x2 = 11.694444447

Factor a perfect square on the left side:
(x + 3.166666667)(x + 3.166666667) = 11.694444447

Calculate the square root of the right side: 3.419714088

Break this problem into two subproblems by setting 
(x + 3.166666667) equal to 3.419714088 and -3.419714088.


Subproblem 1
x + 3.166666667 = 3.419714088

Simplifying
x + 3.166666667 = 3.419714088

Reorder the terms:
3.166666667 + x = 3.419714088

Solving
3.166666667 + x = 3.419714088

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = 3.419714088 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = 3.419714088 + -3.166666667
x = 3.419714088 + -3.166666667

Combine like terms: 3.419714088 + -3.166666667 = 0.253047421
x = 0.253047421

Simplifying
x = 0.253047421


Subproblem 2
x + 3.166666667 = -3.419714088

Simplifying
x + 3.166666667 = -3.419714088

Reorder the terms:
3.166666667 + x = -3.419714088

Solving
3.166666667 + x = -3.419714088

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = -3.419714088 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = -3.419714088 + -3.166666667
x = -3.419714088 + -3.166666667

Combine like terms: -3.419714088 + -3.166666667 = -6.586380755
x = -6.586380755

Simplifying
x = -6.586380755


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.253047421, -6.586380755}
Solution
x = {0.253047421, -6.586380755}

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