3x^2+17x+9=0

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Solution for 3x^2+17x+9=0 equation: 


Simplifying
3x2 + 17x + 9 = 0

Reorder the terms:
9 + 17x + 3x2 = 0

Solving
9 + 17x + 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'.
3 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5.666666667x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 5.666666667x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5.666666667x + x2 = 0 + -3
5.666666667x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
5.666666667x + x2 = -3

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = -3 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -3 + 8.027777782

Combine like terms: -3 + 8.027777782 = 5.027777782
8.027777782 + 5.666666667x + x2 = 5.027777782

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 5.027777782

Calculate the square root of the right side: 2.242270675

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 2.242270675 and -2.242270675.


Subproblem 1
x + 2.833333334 = 2.242270675

Simplifying
x + 2.833333334 = 2.242270675

Reorder the terms:
2.833333334 + x = 2.242270675

Solving
2.833333334 + x = 2.242270675

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = 2.242270675 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 2.242270675 + -2.833333334
x = 2.242270675 + -2.833333334

Combine like terms: 2.242270675 + -2.833333334 = -0.591062659
x = -0.591062659

Simplifying
x = -0.591062659


Subproblem 2
x + 2.833333334 = -2.242270675

Simplifying
x + 2.833333334 = -2.242270675

Reorder the terms:
2.833333334 + x = -2.242270675

Solving
2.833333334 + x = -2.242270675

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = -2.242270675 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -2.242270675 + -2.833333334
x = -2.242270675 + -2.833333334

Combine like terms: -2.242270675 + -2.833333334 = -5.075604009
x = -5.075604009

Simplifying
x = -5.075604009


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.591062659, -5.075604009}

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