0.6x^2+7x+20=0

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Solution for 0.6x^2+7x+20=0 equation: 


Simplifying
0.6x2 + 7x + 20 = 0

Reorder the terms:
20 + 7x + 0.6x2 = 0

Solving
20 + 7x + 0.6x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.6'.
33.33333333 + 11.66666667x + x2 = 0

Move the constant term to the right:

Add '-33.33333333' to each side of the equation.
33.33333333 + 11.66666667x + -33.33333333 + x2 = 0 + -33.33333333

Reorder the terms:
33.33333333 + -33.33333333 + 11.66666667x + x2 = 0 + -33.33333333

Combine like terms: 33.33333333 + -33.33333333 = 0.00000000
0.00000000 + 11.66666667x + x2 = 0 + -33.33333333
11.66666667x + x2 = 0 + -33.33333333

Combine like terms: 0 + -33.33333333 = -33.33333333
11.66666667x + x2 = -33.33333333

The x term is 11.66666667x.  Take half its coefficient (5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
11.66666667x + 34.02777780 + x2 = -33.33333333 + 34.02777780

Reorder the terms:
34.02777780 + 11.66666667x + x2 = -33.33333333 + 34.02777780

Combine like terms: -33.33333333 + 34.02777780 = 0.69444447
34.02777780 + 11.66666667x + x2 = 0.69444447

Factor a perfect square on the left side:
(x + 5.833333335)(x + 5.833333335) = 0.69444447

Calculate the square root of the right side: 0.833333349

Break this problem into two subproblems by setting 
(x + 5.833333335) equal to 0.833333349 and -0.833333349.


Subproblem 1
x + 5.833333335 = 0.833333349

Simplifying
x + 5.833333335 = 0.833333349

Reorder the terms:
5.833333335 + x = 0.833333349

Solving
5.833333335 + x = 0.833333349

Solving for variable 'x'.

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

Add '-5.833333335' to each side of the equation.
5.833333335 + -5.833333335 + x = 0.833333349 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + x = 0.833333349 + -5.833333335
x = 0.833333349 + -5.833333335

Combine like terms: 0.833333349 + -5.833333335 = -4.999999986
x = -4.999999986

Simplifying
x = -4.999999986


Subproblem 2
x + 5.833333335 = -0.833333349

Simplifying
x + 5.833333335 = -0.833333349

Reorder the terms:
5.833333335 + x = -0.833333349

Solving
5.833333335 + x = -0.833333349

Solving for variable 'x'.

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

Add '-5.833333335' to each side of the equation.
5.833333335 + -5.833333335 + x = -0.833333349 + -5.833333335

Combine like terms: 5.833333335 + -5.833333335 = 0.000000000
0.000000000 + x = -0.833333349 + -5.833333335
x = -0.833333349 + -5.833333335

Combine like terms: -0.833333349 + -5.833333335 = -6.666666684
x = -6.666666684

Simplifying
x = -6.666666684


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.999999986, -6.666666684}

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