6x^2+38x+25=0

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Solution for 6x^2+38x+25=0 equation: 


Simplifying
6x2 + 38x + 25 = 0

Reorder the terms:
25 + 38x + 6x2 = 0

Solving
25 + 38x + 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'.
4.166666667 + 6.333333333x + x2 = 0

Move the constant term to the right:

Add '-4.166666667' to each side of the equation.
4.166666667 + 6.333333333x + -4.166666667 + x2 = 0 + -4.166666667

Reorder the terms:
4.166666667 + -4.166666667 + 6.333333333x + x2 = 0 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + 6.333333333x + x2 = 0 + -4.166666667
6.333333333x + x2 = 0 + -4.166666667

Combine like terms: 0 + -4.166666667 = -4.166666667
6.333333333x + x2 = -4.166666667

The x term is 6.333333333x.  Take half its coefficient (3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
6.333333333x + 10.02777778 + x2 = -4.166666667 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333x + x2 = -4.166666667 + 10.02777778

Combine like terms: -4.166666667 + 10.02777778 = 5.861111113
10.02777778 + 6.333333333x + x2 = 5.861111113

Factor a perfect square on the left side:
(x + 3.166666667)(x + 3.166666667) = 5.861111113

Calculate the square root of the right side: 2.420973175

Break this problem into two subproblems by setting 
(x + 3.166666667) equal to 2.420973175 and -2.420973175.


Subproblem 1
x + 3.166666667 = 2.420973175

Simplifying
x + 3.166666667 = 2.420973175

Reorder the terms:
3.166666667 + x = 2.420973175

Solving
3.166666667 + x = 2.420973175

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = 2.420973175 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = 2.420973175 + -3.166666667
x = 2.420973175 + -3.166666667

Combine like terms: 2.420973175 + -3.166666667 = -0.745693492
x = -0.745693492

Simplifying
x = -0.745693492


Subproblem 2
x + 3.166666667 = -2.420973175

Simplifying
x + 3.166666667 = -2.420973175

Reorder the terms:
3.166666667 + x = -2.420973175

Solving
3.166666667 + x = -2.420973175

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = -2.420973175 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = -2.420973175 + -3.166666667
x = -2.420973175 + -3.166666667

Combine like terms: -2.420973175 + -3.166666667 = -5.587639842
x = -5.587639842

Simplifying
x = -5.587639842


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.745693492, -5.587639842}

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