x^2+9x+3=0

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Solution for x^2+9x+3=0 equation: 


Simplifying
x2 + 9x + 3 = 0

Reorder the terms:
3 + 9x + x2 = 0

Solving
3 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 9x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 9x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 9x + x2 = 0 + -3
9x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
9x + x2 = -3

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -3 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -3 + 20.25

Combine like terms: -3 + 20.25 = 17.25
20.25 + 9x + x2 = 17.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + 4.5 = 4.153311931

Simplifying
x + 4.5 = 4.153311931

Reorder the terms:
4.5 + x = 4.153311931

Solving
4.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.153311931 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.153311931 + -4.5
x = 4.153311931 + -4.5

Combine like terms: 4.153311931 + -4.5 = -0.346688069
x = -0.346688069

Simplifying
x = -0.346688069


Subproblem 2
x + 4.5 = -4.153311931

Simplifying
x + 4.5 = -4.153311931

Reorder the terms:
4.5 + x = -4.153311931

Solving
4.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.153311931 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.153311931 + -4.5
x = -4.153311931 + -4.5

Combine like terms: -4.153311931 + -4.5 = -8.653311931
x = -8.653311931

Simplifying
x = -8.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.346688069, -8.653311931}

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