6x^2+20x+-385=0

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Solution for 6x^2+20x+-385=0 equation: 


Simplifying
6x2 + 20x + -385 = 0

Reorder the terms:
-385 + 20x + 6x2 = 0

Solving
-385 + 20x + 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'.
-64.16666667 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '64.16666667' to each side of the equation.
-64.16666667 + 3.333333333x + 64.16666667 + x2 = 0 + 64.16666667

Reorder the terms:
-64.16666667 + 64.16666667 + 3.333333333x + x2 = 0 + 64.16666667

Combine like terms: -64.16666667 + 64.16666667 = 0.00000000
0.00000000 + 3.333333333x + x2 = 0 + 64.16666667
3.333333333x + x2 = 0 + 64.16666667

Combine like terms: 0 + 64.16666667 = 64.16666667
3.333333333x + x2 = 64.16666667

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 64.16666667 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 64.16666667 + 2.777777779

Combine like terms: 64.16666667 + 2.777777779 = 66.944444449
2.777777779 + 3.333333333x + x2 = 66.944444449

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 66.944444449

Calculate the square root of the right side: 8.181958473

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 8.181958473 and -8.181958473.


Subproblem 1
x + 1.666666667 = 8.181958473

Simplifying
x + 1.666666667 = 8.181958473

Reorder the terms:
1.666666667 + x = 8.181958473

Solving
1.666666667 + x = 8.181958473

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 8.181958473 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 8.181958473 + -1.666666667
x = 8.181958473 + -1.666666667

Combine like terms: 8.181958473 + -1.666666667 = 6.515291806
x = 6.515291806

Simplifying
x = 6.515291806


Subproblem 2
x + 1.666666667 = -8.181958473

Simplifying
x + 1.666666667 = -8.181958473

Reorder the terms:
1.666666667 + x = -8.181958473

Solving
1.666666667 + x = -8.181958473

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -8.181958473 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -8.181958473 + -1.666666667
x = -8.181958473 + -1.666666667

Combine like terms: -8.181958473 + -1.666666667 = -9.84862514
x = -9.84862514

Simplifying
x = -9.84862514


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.515291806, -9.84862514}

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