3x^2+17x+7=0

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Solution for 3x^2+17x+7=0 equation: 


Simplifying
3x2 + 17x + 7 = 0

Reorder the terms:
7 + 17x + 3x2 = 0

Solving
7 + 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'.
2.333333333 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 5.666666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 5.666666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 5.666666667x + x2 = 0 + -2.333333333
5.666666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
5.666666667x + x2 = -2.333333333

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 = -2.333333333 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = -2.333333333 + 8.027777782

Combine like terms: -2.333333333 + 8.027777782 = 5.694444449
8.027777782 + 5.666666667x + x2 = 5.694444449

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 5.694444449

Calculate the square root of the right side: 2.386303512

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 2.386303512 and -2.386303512.


Subproblem 1
x + 2.833333334 = 2.386303512

Simplifying
x + 2.833333334 = 2.386303512

Reorder the terms:
2.833333334 + x = 2.386303512

Solving
2.833333334 + x = 2.386303512

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 = 2.386303512 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 2.386303512 + -2.833333334
x = 2.386303512 + -2.833333334

Combine like terms: 2.386303512 + -2.833333334 = -0.447029822
x = -0.447029822

Simplifying
x = -0.447029822


Subproblem 2
x + 2.833333334 = -2.386303512

Simplifying
x + 2.833333334 = -2.386303512

Reorder the terms:
2.833333334 + x = -2.386303512

Solving
2.833333334 + x = -2.386303512

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 = -2.386303512 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -2.386303512 + -2.833333334
x = -2.386303512 + -2.833333334

Combine like terms: -2.386303512 + -2.833333334 = -5.219636846
x = -5.219636846

Simplifying
x = -5.219636846


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.447029822, -5.219636846}

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