3x^2+17x+3=0

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


Simplifying
3x2 + 17x + 3 = 0

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

Solving
3 + 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'.
1 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 5.666666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 5.666666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5.666666667x + x2 = 0 + -1
5.666666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
5.666666667x + x2 = -1

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 = -1 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -1 + 8.027777782

Combine like terms: -1 + 8.027777782 = 7.027777782
8.027777782 + 5.666666667x + x2 = 7.027777782

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 7.027777782

Calculate the square root of the right side: 2.650995621

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 2.650995621 and -2.650995621.


Subproblem 1
x + 2.833333334 = 2.650995621

Simplifying
x + 2.833333334 = 2.650995621

Reorder the terms:
2.833333334 + x = 2.650995621

Solving
2.833333334 + x = 2.650995621

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 = 2.650995621 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 2.650995621 + -2.833333334
x = 2.650995621 + -2.833333334

Combine like terms: 2.650995621 + -2.833333334 = -0.182337713
x = -0.182337713

Simplifying
x = -0.182337713


Subproblem 2
x + 2.833333334 = -2.650995621

Simplifying
x + 2.833333334 = -2.650995621

Reorder the terms:
2.833333334 + x = -2.650995621

Solving
2.833333334 + x = -2.650995621

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 = -2.650995621 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -2.650995621 + -2.833333334
x = -2.650995621 + -2.833333334

Combine like terms: -2.650995621 + -2.833333334 = -5.484328955
x = -5.484328955

Simplifying
x = -5.484328955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.182337713, -5.484328955}

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