0.3x^2+9x+3.2=0

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Solution for 0.3x^2+9x+3.2=0 equation: 


Simplifying
0.3x2 + 9x + 3.2 = 0

Reorder the terms:
3.2 + 9x + 0.3x2 = 0

Solving
3.2 + 9x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
10.66666667 + 30x + x2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + 30x + -10.66666667 + x2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + 30x + x2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + 30x + x2 = 0 + -10.66666667
30x + x2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
30x + x2 = -10.66666667

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -10.66666667 + 225

Reorder the terms:
225 + 30x + x2 = -10.66666667 + 225

Combine like terms: -10.66666667 + 225 = 214.33333333
225 + 30x + x2 = 214.33333333

Factor a perfect square on the left side:
(x + 15)(x + 15) = 214.33333333

Calculate the square root of the right side: 14.640127504

Break this problem into two subproblems by setting 
(x + 15) equal to 14.640127504 and -14.640127504.


Subproblem 1
x + 15 = 14.640127504

Simplifying
x + 15 = 14.640127504

Reorder the terms:
15 + x = 14.640127504

Solving
15 + x = 14.640127504

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 14.640127504 + -15

Combine like terms: 15 + -15 = 0
0 + x = 14.640127504 + -15
x = 14.640127504 + -15

Combine like terms: 14.640127504 + -15 = -0.359872496
x = -0.359872496

Simplifying
x = -0.359872496


Subproblem 2
x + 15 = -14.640127504

Simplifying
x + 15 = -14.640127504

Reorder the terms:
15 + x = -14.640127504

Solving
15 + x = -14.640127504

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -14.640127504 + -15

Combine like terms: 15 + -15 = 0
0 + x = -14.640127504 + -15
x = -14.640127504 + -15

Combine like terms: -14.640127504 + -15 = -29.640127504
x = -29.640127504

Simplifying
x = -29.640127504


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.359872496, -29.640127504}

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