6x^2+25x+20=0

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Solution for 6x^2+25x+20=0 equation: 


Simplifying
6x2 + 25x + 20 = 0

Reorder the terms:
20 + 25x + 6x2 = 0

Solving
20 + 25x + 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 + 4.166666667x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 4.166666667x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 4.166666667x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 4.166666667x + x2 = 0 + -3.333333333
4.166666667x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
4.166666667x + x2 = -3.333333333

The x term is 4.166666667x.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667x + 4.340277781 + x2 = -3.333333333 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667x + x2 = -3.333333333 + 4.340277781

Combine like terms: -3.333333333 + 4.340277781 = 1.006944448
4.340277781 + 4.166666667x + x2 = 1.006944448

Factor a perfect square on the left side:
(x + 2.083333334)(x + 2.083333334) = 1.006944448

Calculate the square root of the right side: 1.003466217

Break this problem into two subproblems by setting 
(x + 2.083333334) equal to 1.003466217 and -1.003466217.


Subproblem 1
x + 2.083333334 = 1.003466217

Simplifying
x + 2.083333334 = 1.003466217

Reorder the terms:
2.083333334 + x = 1.003466217

Solving
2.083333334 + x = 1.003466217

Solving for variable 'x'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x = 1.003466217 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x = 1.003466217 + -2.083333334
x = 1.003466217 + -2.083333334

Combine like terms: 1.003466217 + -2.083333334 = -1.079867117
x = -1.079867117

Simplifying
x = -1.079867117


Subproblem 2
x + 2.083333334 = -1.003466217

Simplifying
x + 2.083333334 = -1.003466217

Reorder the terms:
2.083333334 + x = -1.003466217

Solving
2.083333334 + x = -1.003466217

Solving for variable 'x'.

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

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x = -1.003466217 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x = -1.003466217 + -2.083333334
x = -1.003466217 + -2.083333334

Combine like terms: -1.003466217 + -2.083333334 = -3.086799551
x = -3.086799551

Simplifying
x = -3.086799551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.079867117, -3.086799551}

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