9x^2+30x+20=0

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Solution for 9x^2+30x+20=0 equation: 


Simplifying
9x2 + 30x + 20 = 0

Reorder the terms:
20 + 30x + 9x2 = 0

Solving
20 + 30x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
2.222222222 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.222222222' to each side of the equation.
2.222222222 + 3.333333333x + -2.222222222 + x2 = 0 + -2.222222222

Reorder the terms:
2.222222222 + -2.222222222 + 3.333333333x + x2 = 0 + -2.222222222

Combine like terms: 2.222222222 + -2.222222222 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + -2.222222222
3.333333333x + x2 = 0 + -2.222222222

Combine like terms: 0 + -2.222222222 = -2.222222222
3.333333333x + x2 = -2.222222222

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -2.222222222 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -2.222222222 + 2.777777779

Combine like terms: -2.222222222 + 2.777777779 = 0.555555557
2.777777779 + 3.333333333x + x2 = 0.555555557

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 0.555555557

Calculate the square root of the right side: 0.745355993

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 0.745355993 and -0.745355993.


Subproblem 1
x + 1.666666667 = 0.745355993

Simplifying
x + 1.666666667 = 0.745355993

Reorder the terms:
1.666666667 + x = 0.745355993

Solving
1.666666667 + x = 0.745355993

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 0.745355993 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 0.745355993 + -1.666666667
x = 0.745355993 + -1.666666667

Combine like terms: 0.745355993 + -1.666666667 = -0.921310674
x = -0.921310674

Simplifying
x = -0.921310674


Subproblem 2
x + 1.666666667 = -0.745355993

Simplifying
x + 1.666666667 = -0.745355993

Reorder the terms:
1.666666667 + x = -0.745355993

Solving
1.666666667 + x = -0.745355993

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -0.745355993 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -0.745355993 + -1.666666667
x = -0.745355993 + -1.666666667

Combine like terms: -0.745355993 + -1.666666667 = -2.41202266
x = -2.41202266

Simplifying
x = -2.41202266


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.921310674, -2.41202266}

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