2x+x^2+3(4x)+17=0

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Solution for 2x+x^2+3(4x)+17=0 equation: 


Simplifying
2x + x2 + 3(4x) + 17 = 0

Remove parenthesis around (4x)
2x + x2 + 3 * 4x + 17 = 0

Multiply 3 * 4
2x + x2 + 12x + 17 = 0

Reorder the terms:
17 + 2x + 12x + x2 = 0

Combine like terms: 2x + 12x = 14x
17 + 14x + x2 = 0

Solving
17 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 14x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 14x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 14x + x2 = 0 + -17
14x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
14x + x2 = -17

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -17 + 49

Reorder the terms:
49 + 14x + x2 = -17 + 49

Combine like terms: -17 + 49 = 32
49 + 14x + x2 = 32

Factor a perfect square on the left side:
(x + 7)(x + 7) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 7) equal to 5.656854249 and -5.656854249.


Subproblem 1
x + 7 = 5.656854249

Simplifying
x + 7 = 5.656854249

Reorder the terms:
7 + x = 5.656854249

Solving
7 + x = 5.656854249

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 5.656854249 + -7

Combine like terms: 7 + -7 = 0
0 + x = 5.656854249 + -7
x = 5.656854249 + -7

Combine like terms: 5.656854249 + -7 = -1.343145751
x = -1.343145751

Simplifying
x = -1.343145751


Subproblem 2
x + 7 = -5.656854249

Simplifying
x + 7 = -5.656854249

Reorder the terms:
7 + x = -5.656854249

Solving
7 + x = -5.656854249

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -5.656854249 + -7

Combine like terms: 7 + -7 = 0
0 + x = -5.656854249 + -7
x = -5.656854249 + -7

Combine like terms: -5.656854249 + -7 = -12.656854249
x = -12.656854249

Simplifying
x = -12.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.343145751, -12.656854249}

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