3x^2+18x+34=9

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Solution for 3x^2+18x+34=9 equation: 


Simplifying
3x2 + 18x + 34 = 9

Reorder the terms:
34 + 18x + 3x2 = 9

Solving
34 + 18x + 3x2 = 9

Solving for variable 'x'.

Reorder the terms:
34 + -9 + 18x + 3x2 = 9 + -9

Combine like terms: 34 + -9 = 25
25 + 18x + 3x2 = 9 + -9

Combine like terms: 9 + -9 = 0
25 + 18x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
8.333333333 + 6x + x2 = 0

Move the constant term to the right:

Add '-8.333333333' to each side of the equation.
8.333333333 + 6x + -8.333333333 + x2 = 0 + -8.333333333

Reorder the terms:
8.333333333 + -8.333333333 + 6x + x2 = 0 + -8.333333333

Combine like terms: 8.333333333 + -8.333333333 = 0.000000000
0.000000000 + 6x + x2 = 0 + -8.333333333
6x + x2 = 0 + -8.333333333

Combine like terms: 0 + -8.333333333 = -8.333333333
6x + x2 = -8.333333333

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -8.333333333 + 9

Reorder the terms:
9 + 6x + x2 = -8.333333333 + 9

Combine like terms: -8.333333333 + 9 = 0.666666667
9 + 6x + x2 = 0.666666667

Factor a perfect square on the left side:
(x + 3)(x + 3) = 0.666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(x + 3) equal to 0.816496581 and -0.816496581.


Subproblem 1
x + 3 = 0.816496581

Simplifying
x + 3 = 0.816496581

Reorder the terms:
3 + x = 0.816496581

Solving
3 + x = 0.816496581

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 0.816496581 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0.816496581 + -3
x = 0.816496581 + -3

Combine like terms: 0.816496581 + -3 = -2.183503419
x = -2.183503419

Simplifying
x = -2.183503419


Subproblem 2
x + 3 = -0.816496581

Simplifying
x + 3 = -0.816496581

Reorder the terms:
3 + x = -0.816496581

Solving
3 + x = -0.816496581

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -0.816496581 + -3

Combine like terms: 3 + -3 = 0
0 + x = -0.816496581 + -3
x = -0.816496581 + -3

Combine like terms: -0.816496581 + -3 = -3.816496581
x = -3.816496581

Simplifying
x = -3.816496581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.183503419, -3.816496581}

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