3x^2+18x+35x=8

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Solution for 3x^2+18x+35x=8 equation: 


Simplifying
3x2 + 18x + 35x = 8

Reorder the terms:
18x + 35x + 3x2 = 8

Combine like terms: 18x + 35x = 53x
53x + 3x2 = 8

Solving
53x + 3x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 53x + 3x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 53x + 3x2 = 0

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

Divide each side by '3'.
-2.666666667 + 17.66666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 17.66666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 17.66666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 17.66666667x + x2 = 0 + 2.666666667
17.66666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
17.66666667x + x2 = 2.666666667

The x term is 17.66666667x.  Take half its coefficient (8.833333335).
Square it (78.02777781) and add it to both sides.

Add '78.02777781' to each side of the equation.
17.66666667x + 78.02777781 + x2 = 2.666666667 + 78.02777781

Reorder the terms:
78.02777781 + 17.66666667x + x2 = 2.666666667 + 78.02777781

Combine like terms: 2.666666667 + 78.02777781 = 80.694444477
78.02777781 + 17.66666667x + x2 = 80.694444477

Factor a perfect square on the left side:
(x + 8.833333335)(x + 8.833333335) = 80.694444477

Calculate the square root of the right side: 8.983008654

Break this problem into two subproblems by setting 
(x + 8.833333335) equal to 8.983008654 and -8.983008654.


Subproblem 1
x + 8.833333335 = 8.983008654

Simplifying
x + 8.833333335 = 8.983008654

Reorder the terms:
8.833333335 + x = 8.983008654

Solving
8.833333335 + x = 8.983008654

Solving for variable 'x'.

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

Add '-8.833333335' to each side of the equation.
8.833333335 + -8.833333335 + x = 8.983008654 + -8.833333335

Combine like terms: 8.833333335 + -8.833333335 = 0.000000000
0.000000000 + x = 8.983008654 + -8.833333335
x = 8.983008654 + -8.833333335

Combine like terms: 8.983008654 + -8.833333335 = 0.149675319
x = 0.149675319

Simplifying
x = 0.149675319


Subproblem 2
x + 8.833333335 = -8.983008654

Simplifying
x + 8.833333335 = -8.983008654

Reorder the terms:
8.833333335 + x = -8.983008654

Solving
8.833333335 + x = -8.983008654

Solving for variable 'x'.

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

Add '-8.833333335' to each side of the equation.
8.833333335 + -8.833333335 + x = -8.983008654 + -8.833333335

Combine like terms: 8.833333335 + -8.833333335 = 0.000000000
0.000000000 + x = -8.983008654 + -8.833333335
x = -8.983008654 + -8.833333335

Combine like terms: -8.983008654 + -8.833333335 = -17.816341989
x = -17.816341989

Simplifying
x = -17.816341989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.149675319, -17.816341989}

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