a^2+10a+14=0

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Solution for a^2+10a+14=0 equation: 


Simplifying
a2 + 10a + 14 = 0

Reorder the terms:
14 + 10a + a2 = 0

Solving
14 + 10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 10a + -14 + a2 = 0 + -14

Reorder the terms:
14 + -14 + 10a + a2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 10a + a2 = 0 + -14
10a + a2 = 0 + -14

Combine like terms: 0 + -14 = -14
10a + a2 = -14

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = -14 + 25

Reorder the terms:
25 + 10a + a2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + 10a + a2 = 11

Factor a perfect square on the left side:
(a + 5)(a + 5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(a + 5) equal to 3.31662479 and -3.31662479.


Subproblem 1
a + 5 = 3.31662479

Simplifying
a + 5 = 3.31662479

Reorder the terms:
5 + a = 3.31662479

Solving
5 + a = 3.31662479

Solving for variable 'a'.

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

Add '-5' to each side of the equation.
5 + -5 + a = 3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + a = 3.31662479 + -5
a = 3.31662479 + -5

Combine like terms: 3.31662479 + -5 = -1.68337521
a = -1.68337521

Simplifying
a = -1.68337521


Subproblem 2
a + 5 = -3.31662479

Simplifying
a + 5 = -3.31662479

Reorder the terms:
5 + a = -3.31662479

Solving
5 + a = -3.31662479

Solving for variable 'a'.

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

Add '-5' to each side of the equation.
5 + -5 + a = -3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + a = -3.31662479 + -5
a = -3.31662479 + -5

Combine like terms: -3.31662479 + -5 = -8.31662479
a = -8.31662479

Simplifying
a = -8.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-1.68337521, -8.31662479}

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