6x^2+34x-10=0

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Solution for 6x^2+34x-10=0 equation: 


Simplifying
6x2 + 34x + -10 = 0

Reorder the terms:
-10 + 34x + 6x2 = 0

Solving
-10 + 34x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 17x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 17x + 3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 17x + 3x2 = 0

Solving
-5 + 17x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 5.666666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 5.666666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 5.666666667x + x2 = 0 + 1.666666667
5.666666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
5.666666667x + x2 = 1.666666667

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = 1.666666667 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = 1.666666667 + 8.027777782

Combine like terms: 1.666666667 + 8.027777782 = 9.694444449
8.027777782 + 5.666666667x + x2 = 9.694444449

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 9.694444449

Calculate the square root of the right side: 3.113590283

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 3.113590283 and -3.113590283.


Subproblem 1
x + 2.833333334 = 3.113590283

Simplifying
x + 2.833333334 = 3.113590283

Reorder the terms:
2.833333334 + x = 3.113590283

Solving
2.833333334 + x = 3.113590283

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = 3.113590283 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 3.113590283 + -2.833333334
x = 3.113590283 + -2.833333334

Combine like terms: 3.113590283 + -2.833333334 = 0.280256949
x = 0.280256949

Simplifying
x = 0.280256949


Subproblem 2
x + 2.833333334 = -3.113590283

Simplifying
x + 2.833333334 = -3.113590283

Reorder the terms:
2.833333334 + x = -3.113590283

Solving
2.833333334 + x = -3.113590283

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = -3.113590283 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -3.113590283 + -2.833333334
x = -3.113590283 + -2.833333334

Combine like terms: -3.113590283 + -2.833333334 = -5.946923617
x = -5.946923617

Simplifying
x = -5.946923617


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.280256949, -5.946923617}
Solution
x = {0.280256949, -5.946923617}

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