6x^2+35x+20=

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Solution for 6x^2+35x+20= equation: 


Simplifying
6x2 + 35x + 20 = 0

Reorder the terms:
20 + 35x + 6x2 = 0

Solving
20 + 35x + 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'.
3.333333333 + 5.833333333x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 5.833333333x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 5.833333333x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 5.833333333x + x2 = 0 + -3.333333333
5.833333333x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
5.833333333x + x2 = -3.333333333

The x term is 5.833333333x.  Take half its coefficient (2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
5.833333333x + 8.506944446 + x2 = -3.333333333 + 8.506944446

Reorder the terms:
8.506944446 + 5.833333333x + x2 = -3.333333333 + 8.506944446

Combine like terms: -3.333333333 + 8.506944446 = 5.173611113
8.506944446 + 5.833333333x + x2 = 5.173611113

Factor a perfect square on the left side:
(x + 2.916666667)(x + 2.916666667) = 5.173611113

Calculate the square root of the right side: 2.274557344

Break this problem into two subproblems by setting 
(x + 2.916666667) equal to 2.274557344 and -2.274557344.


Subproblem 1
x + 2.916666667 = 2.274557344

Simplifying
x + 2.916666667 = 2.274557344

Reorder the terms:
2.916666667 + x = 2.274557344

Solving
2.916666667 + x = 2.274557344

Solving for variable 'x'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + x = 2.274557344 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + x = 2.274557344 + -2.916666667
x = 2.274557344 + -2.916666667

Combine like terms: 2.274557344 + -2.916666667 = -0.642109323
x = -0.642109323

Simplifying
x = -0.642109323


Subproblem 2
x + 2.916666667 = -2.274557344

Simplifying
x + 2.916666667 = -2.274557344

Reorder the terms:
2.916666667 + x = -2.274557344

Solving
2.916666667 + x = -2.274557344

Solving for variable 'x'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + x = -2.274557344 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + x = -2.274557344 + -2.916666667
x = -2.274557344 + -2.916666667

Combine like terms: -2.274557344 + -2.916666667 = -5.191224011
x = -5.191224011

Simplifying
x = -5.191224011


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.642109323, -5.191224011}

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