x^2+14x+30=0

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Solution for x^2+14x+30=0 equation: 


Simplifying
x2 + 14x + 30 = 0

Reorder the terms:
30 + 14x + x2 = 0

Solving
30 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 14x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 14x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 14x + x2 = 0 + -30
14x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
14x + x2 = -30

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 = -30 + 49

Reorder the terms:
49 + 14x + x2 = -30 + 49

Combine like terms: -30 + 49 = 19
49 + 14x + x2 = 19

Factor a perfect square on the left side:
(x + 7)(x + 7) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + 7) equal to 4.358898944 and -4.358898944.


Subproblem 1
x + 7 = 4.358898944

Simplifying
x + 7 = 4.358898944

Reorder the terms:
7 + x = 4.358898944

Solving
7 + x = 4.358898944

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 = 4.358898944 + -7

Combine like terms: 7 + -7 = 0
0 + x = 4.358898944 + -7
x = 4.358898944 + -7

Combine like terms: 4.358898944 + -7 = -2.641101056
x = -2.641101056

Simplifying
x = -2.641101056


Subproblem 2
x + 7 = -4.358898944

Simplifying
x + 7 = -4.358898944

Reorder the terms:
7 + x = -4.358898944

Solving
7 + x = -4.358898944

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 = -4.358898944 + -7

Combine like terms: 7 + -7 = 0
0 + x = -4.358898944 + -7
x = -4.358898944 + -7

Combine like terms: -4.358898944 + -7 = -11.358898944
x = -11.358898944

Simplifying
x = -11.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.641101056, -11.358898944}

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