x*3x+2*(17x)=42

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Solution for x*3x+2*(17x)=42 equation: 


Simplifying
x * 3x + 2(17x) = 42

Reorder the terms for easier multiplication:
3x * x + 2(17x) = 42

Multiply x * x
3x2 + 2(17x) = 42

Remove parenthesis around (17x)
3x2 + 2 * 17x = 42

Multiply 2 * 17
3x2 + 34x = 42

Reorder the terms:
34x + 3x2 = 42

Solving
34x + 3x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 34x + 3x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 34x + 3x2 = 0

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

Divide each side by '3'.
-14 + 11.33333333x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 11.33333333x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 11.33333333x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 11.33333333x + x2 = 0 + 14
11.33333333x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
11.33333333x + x2 = 14

The x term is 11.33333333x.  Take half its coefficient (5.666666665).
Square it (32.11111109) and add it to both sides.

Add '32.11111109' to each side of the equation.
11.33333333x + 32.11111109 + x2 = 14 + 32.11111109

Reorder the terms:
32.11111109 + 11.33333333x + x2 = 14 + 32.11111109

Combine like terms: 14 + 32.11111109 = 46.11111109
32.11111109 + 11.33333333x + x2 = 46.11111109

Factor a perfect square on the left side:
(x + 5.666666665)(x + 5.666666665) = 46.11111109

Calculate the square root of the right side: 6.790516261

Break this problem into two subproblems by setting 
(x + 5.666666665) equal to 6.790516261 and -6.790516261.


Subproblem 1
x + 5.666666665 = 6.790516261

Simplifying
x + 5.666666665 = 6.790516261

Reorder the terms:
5.666666665 + x = 6.790516261

Solving
5.666666665 + x = 6.790516261

Solving for variable 'x'.

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

Add '-5.666666665' to each side of the equation.
5.666666665 + -5.666666665 + x = 6.790516261 + -5.666666665

Combine like terms: 5.666666665 + -5.666666665 = 0.000000000
0.000000000 + x = 6.790516261 + -5.666666665
x = 6.790516261 + -5.666666665

Combine like terms: 6.790516261 + -5.666666665 = 1.123849596
x = 1.123849596

Simplifying
x = 1.123849596


Subproblem 2
x + 5.666666665 = -6.790516261

Simplifying
x + 5.666666665 = -6.790516261

Reorder the terms:
5.666666665 + x = -6.790516261

Solving
5.666666665 + x = -6.790516261

Solving for variable 'x'.

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

Add '-5.666666665' to each side of the equation.
5.666666665 + -5.666666665 + x = -6.790516261 + -5.666666665

Combine like terms: 5.666666665 + -5.666666665 = 0.000000000
0.000000000 + x = -6.790516261 + -5.666666665
x = -6.790516261 + -5.666666665

Combine like terms: -6.790516261 + -5.666666665 = -12.457182926
x = -12.457182926

Simplifying
x = -12.457182926


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.123849596, -12.457182926}

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