3x^2+6x+2x+4=150

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Solution for 3x^2+6x+2x+4=150 equation: 


Simplifying
3x2 + 6x + 2x + 4 = 150

Reorder the terms:
4 + 6x + 2x + 3x2 = 150

Combine like terms: 6x + 2x = 8x
4 + 8x + 3x2 = 150

Solving
4 + 8x + 3x2 = 150

Solving for variable 'x'.

Reorder the terms:
4 + -150 + 8x + 3x2 = 150 + -150

Combine like terms: 4 + -150 = -146
-146 + 8x + 3x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-146 + 8x + 3x2 = 0

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

Divide each side by '3'.
-48.66666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '48.66666667' to each side of the equation.
-48.66666667 + 2.666666667x + 48.66666667 + x2 = 0 + 48.66666667

Reorder the terms:
-48.66666667 + 48.66666667 + 2.666666667x + x2 = 0 + 48.66666667

Combine like terms: -48.66666667 + 48.66666667 = 0.00000000
0.00000000 + 2.666666667x + x2 = 0 + 48.66666667
2.666666667x + x2 = 0 + 48.66666667

Combine like terms: 0 + 48.66666667 = 48.66666667
2.666666667x + x2 = 48.66666667

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 48.66666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 48.66666667 + 1.777777780

Combine like terms: 48.66666667 + 1.777777780 = 50.44444445
1.777777780 + 2.666666667x + x2 = 50.44444445

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 50.44444445

Calculate the square root of the right side: 7.102425251

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 7.102425251 and -7.102425251.


Subproblem 1
x + 1.333333334 = 7.102425251

Simplifying
x + 1.333333334 = 7.102425251

Reorder the terms:
1.333333334 + x = 7.102425251

Solving
1.333333334 + x = 7.102425251

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 7.102425251 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 7.102425251 + -1.333333334
x = 7.102425251 + -1.333333334

Combine like terms: 7.102425251 + -1.333333334 = 5.769091917
x = 5.769091917

Simplifying
x = 5.769091917


Subproblem 2
x + 1.333333334 = -7.102425251

Simplifying
x + 1.333333334 = -7.102425251

Reorder the terms:
1.333333334 + x = -7.102425251

Solving
1.333333334 + x = -7.102425251

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -7.102425251 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -7.102425251 + -1.333333334
x = -7.102425251 + -1.333333334

Combine like terms: -7.102425251 + -1.333333334 = -8.435758585
x = -8.435758585

Simplifying
x = -8.435758585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.769091917, -8.435758585}

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