3x^2+25x+32=0

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Solution for 3x^2+25x+32=0 equation: 


Simplifying
3x2 + 25x + 32 = 0

Reorder the terms:
32 + 25x + 3x2 = 0

Solving
32 + 25x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
10.66666667 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + 8.333333333x + -10.66666667 + x2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + 8.333333333x + x2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + 8.333333333x + x2 = 0 + -10.66666667
8.333333333x + x2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
8.333333333x + x2 = -10.66666667

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 = -10.66666667 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = -10.66666667 + 17.36111111

Combine like terms: -10.66666667 + 17.36111111 = 6.69444444
17.36111111 + 8.333333333x + x2 = 6.69444444

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 6.69444444

Calculate the square root of the right side: 2.587362449

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 2.587362449 and -2.587362449.


Subproblem 1
x + 4.166666667 = 2.587362449

Simplifying
x + 4.166666667 = 2.587362449

Reorder the terms:
4.166666667 + x = 2.587362449

Solving
4.166666667 + x = 2.587362449

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 = 2.587362449 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = 2.587362449 + -4.166666667
x = 2.587362449 + -4.166666667

Combine like terms: 2.587362449 + -4.166666667 = -1.579304218
x = -1.579304218

Simplifying
x = -1.579304218


Subproblem 2
x + 4.166666667 = -2.587362449

Simplifying
x + 4.166666667 = -2.587362449

Reorder the terms:
4.166666667 + x = -2.587362449

Solving
4.166666667 + x = -2.587362449

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 = -2.587362449 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = -2.587362449 + -4.166666667
x = -2.587362449 + -4.166666667

Combine like terms: -2.587362449 + -4.166666667 = -6.754029116
x = -6.754029116

Simplifying
x = -6.754029116


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.579304218, -6.754029116}

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