5-2x(x+6)=14

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Solution for 5-2x(x+6)=14 equation: 


Simplifying
5 + -2x(x + 6) = 14

Reorder the terms:
5 + -2x(6 + x) = 14
5 + (6 * -2x + x * -2x) = 14
5 + (-12x + -2x2) = 14

Solving
5 + -12x + -2x2 = 14

Solving for variable 'x'.

Reorder the terms:
5 + -14 + -12x + -2x2 = 14 + -14

Combine like terms: 5 + -14 = -9
-9 + -12x + -2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-9 + -12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 12x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + 12x + 2x2)' equal to zero and attempt to solve:

Simplifying
9 + 12x + 2x2 = 0

Solving
9 + 12x + 2x2 = 0

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

Divide each side by '2'.
4.5 + 6x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 6x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 6x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 6x + x2 = 0 + -4.5
6x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
6x + x2 = -4.5

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 = -4.5 + 9

Reorder the terms:
9 + 6x + x2 = -4.5 + 9

Combine like terms: -4.5 + 9 = 4.5
9 + 6x + x2 = 4.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + 3) equal to 2.121320344 and -2.121320344.


Subproblem 1
x + 3 = 2.121320344

Simplifying
x + 3 = 2.121320344

Reorder the terms:
3 + x = 2.121320344

Solving
3 + x = 2.121320344

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 = 2.121320344 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.121320344 + -3
x = 2.121320344 + -3

Combine like terms: 2.121320344 + -3 = -0.878679656
x = -0.878679656

Simplifying
x = -0.878679656


Subproblem 2
x + 3 = -2.121320344

Simplifying
x + 3 = -2.121320344

Reorder the terms:
3 + x = -2.121320344

Solving
3 + x = -2.121320344

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 = -2.121320344 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.121320344 + -3
x = -2.121320344 + -3

Combine like terms: -2.121320344 + -3 = -5.121320344
x = -5.121320344

Simplifying
x = -5.121320344


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.878679656, -5.121320344}
Solution
x = {-0.878679656, -5.121320344}

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