7x+2x(x+6)=39

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Solution for 7x+2x(x+6)=39 equation: 


Simplifying
7x + 2x(x + 6) = 39

Reorder the terms:
7x + 2x(6 + x) = 39
7x + (6 * 2x + x * 2x) = 39
7x + (12x + 2x2) = 39

Combine like terms: 7x + 12x = 19x
19x + 2x2 = 39

Solving
19x + 2x2 = 39

Solving for variable 'x'.

Reorder the terms:
-39 + 19x + 2x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-39 + 19x + 2x2 = 0

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

Divide each side by '2'.
-19.5 + 9.5x + x2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + 9.5x + 19.5 + x2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + 9.5x + x2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + 9.5x + x2 = 0 + 19.5
9.5x + x2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
9.5x + x2 = 19.5

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = 19.5 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = 19.5 + 22.5625

Combine like terms: 19.5 + 22.5625 = 42.0625
22.5625 + 9.5x + x2 = 42.0625

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 42.0625

Calculate the square root of the right side: 6.485560886

Break this problem into two subproblems by setting 
(x + 4.75) equal to 6.485560886 and -6.485560886.


Subproblem 1
x + 4.75 = 6.485560886

Simplifying
x + 4.75 = 6.485560886

Reorder the terms:
4.75 + x = 6.485560886

Solving
4.75 + x = 6.485560886

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = 6.485560886 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = 6.485560886 + -4.75
x = 6.485560886 + -4.75

Combine like terms: 6.485560886 + -4.75 = 1.735560886
x = 1.735560886

Simplifying
x = 1.735560886


Subproblem 2
x + 4.75 = -6.485560886

Simplifying
x + 4.75 = -6.485560886

Reorder the terms:
4.75 + x = -6.485560886

Solving
4.75 + x = -6.485560886

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = -6.485560886 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = -6.485560886 + -4.75
x = -6.485560886 + -4.75

Combine like terms: -6.485560886 + -4.75 = -11.235560886
x = -11.235560886

Simplifying
x = -11.235560886


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.735560886, -11.235560886}

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