x^2+14x+32=0

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Solution for x^2+14x+32=0 equation: 


Simplifying
x2 + 14x + 32 = 0

Reorder the terms:
32 + 14x + x2 = 0

Solving
32 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + 14x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + 14x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 14x + x2 = 0 + -32
14x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
14x + x2 = -32

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 = -32 + 49

Reorder the terms:
49 + 14x + x2 = -32 + 49

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

Factor a perfect square on the left side:
(x + 7)(x + 7) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 7) equal to 4.123105626 and -4.123105626.


Subproblem 1
x + 7 = 4.123105626

Simplifying
x + 7 = 4.123105626

Reorder the terms:
7 + x = 4.123105626

Solving
7 + x = 4.123105626

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 = 4.123105626 + -7

Combine like terms: 7 + -7 = 0
0 + x = 4.123105626 + -7
x = 4.123105626 + -7

Combine like terms: 4.123105626 + -7 = -2.876894374
x = -2.876894374

Simplifying
x = -2.876894374


Subproblem 2
x + 7 = -4.123105626

Simplifying
x + 7 = -4.123105626

Reorder the terms:
7 + x = -4.123105626

Solving
7 + x = -4.123105626

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 = -4.123105626 + -7

Combine like terms: 7 + -7 = 0
0 + x = -4.123105626 + -7
x = -4.123105626 + -7

Combine like terms: -4.123105626 + -7 = -11.123105626
x = -11.123105626

Simplifying
x = -11.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.876894374, -11.123105626}

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