6x^2+50x+85=0

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Solution for 6x^2+50x+85=0 equation: 


Simplifying
6x2 + 50x + 85 = 0

Reorder the terms:
85 + 50x + 6x2 = 0

Solving
85 + 50x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
14.16666667 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '-14.16666667' to each side of the equation.
14.16666667 + 8.333333333x + -14.16666667 + x2 = 0 + -14.16666667

Reorder the terms:
14.16666667 + -14.16666667 + 8.333333333x + x2 = 0 + -14.16666667

Combine like terms: 14.16666667 + -14.16666667 = 0.00000000
0.00000000 + 8.333333333x + x2 = 0 + -14.16666667
8.333333333x + x2 = 0 + -14.16666667

Combine like terms: 0 + -14.16666667 = -14.16666667
8.333333333x + x2 = -14.16666667

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = -14.16666667 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = -14.16666667 + 17.36111111

Combine like terms: -14.16666667 + 17.36111111 = 3.19444444
17.36111111 + 8.333333333x + x2 = 3.19444444

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 3.19444444

Calculate the square root of the right side: 1.787300881

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 1.787300881 and -1.787300881.


Subproblem 1
x + 4.166666667 = 1.787300881

Simplifying
x + 4.166666667 = 1.787300881

Reorder the terms:
4.166666667 + x = 1.787300881

Solving
4.166666667 + x = 1.787300881

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = 1.787300881 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = 1.787300881 + -4.166666667
x = 1.787300881 + -4.166666667

Combine like terms: 1.787300881 + -4.166666667 = -2.379365786
x = -2.379365786

Simplifying
x = -2.379365786


Subproblem 2
x + 4.166666667 = -1.787300881

Simplifying
x + 4.166666667 = -1.787300881

Reorder the terms:
4.166666667 + x = -1.787300881

Solving
4.166666667 + x = -1.787300881

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = -1.787300881 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = -1.787300881 + -4.166666667
x = -1.787300881 + -4.166666667

Combine like terms: -1.787300881 + -4.166666667 = -5.953967548
x = -5.953967548

Simplifying
x = -5.953967548


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.379365786, -5.953967548}

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