3x^2+17x+5=0

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Solution for 3x^2+17x+5=0 equation: 


Simplifying
3x2 + 17x + 5 = 0

Reorder the terms:
5 + 17x + 3x2 = 0

Solving
5 + 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'.
1.666666667 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 5.666666667x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 5.666666667x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 5.666666667x + x2 = 0 + -1.666666667
5.666666667x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
5.666666667x + x2 = -1.666666667

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 = -1.666666667 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -1.666666667 + 8.027777782

Combine like terms: -1.666666667 + 8.027777782 = 6.361111115
8.027777782 + 5.666666667x + x2 = 6.361111115

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 6.361111115

Calculate the square root of the right side: 2.522124326

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 2.522124326 and -2.522124326.


Subproblem 1
x + 2.833333334 = 2.522124326

Simplifying
x + 2.833333334 = 2.522124326

Reorder the terms:
2.833333334 + x = 2.522124326

Solving
2.833333334 + x = 2.522124326

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 = 2.522124326 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 2.522124326 + -2.833333334
x = 2.522124326 + -2.833333334

Combine like terms: 2.522124326 + -2.833333334 = -0.311209008
x = -0.311209008

Simplifying
x = -0.311209008


Subproblem 2
x + 2.833333334 = -2.522124326

Simplifying
x + 2.833333334 = -2.522124326

Reorder the terms:
2.833333334 + x = -2.522124326

Solving
2.833333334 + x = -2.522124326

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 = -2.522124326 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -2.522124326 + -2.833333334
x = -2.522124326 + -2.833333334

Combine like terms: -2.522124326 + -2.833333334 = -5.35545766
x = -5.35545766

Simplifying
x = -5.35545766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.311209008, -5.35545766}

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