a^2+14a-18=0

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Solution for a^2+14a-18=0 equation: 


Simplifying
a2 + 14a + -18 = 0

Reorder the terms:
-18 + 14a + a2 = 0

Solving
-18 + 14a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 14a + 18 + a2 = 0 + 18

Reorder the terms:
-18 + 18 + 14a + a2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 14a + a2 = 0 + 18
14a + a2 = 0 + 18

Combine like terms: 0 + 18 = 18
14a + a2 = 18

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

Add '49' to each side of the equation.
14a + 49 + a2 = 18 + 49

Reorder the terms:
49 + 14a + a2 = 18 + 49

Combine like terms: 18 + 49 = 67
49 + 14a + a2 = 67

Factor a perfect square on the left side:
(a + 7)(a + 7) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(a + 7) equal to 8.185352772 and -8.185352772.


Subproblem 1
a + 7 = 8.185352772

Simplifying
a + 7 = 8.185352772

Reorder the terms:
7 + a = 8.185352772

Solving
7 + a = 8.185352772

Solving for variable 'a'.

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

Add '-7' to each side of the equation.
7 + -7 + a = 8.185352772 + -7

Combine like terms: 7 + -7 = 0
0 + a = 8.185352772 + -7
a = 8.185352772 + -7

Combine like terms: 8.185352772 + -7 = 1.185352772
a = 1.185352772

Simplifying
a = 1.185352772


Subproblem 2
a + 7 = -8.185352772

Simplifying
a + 7 = -8.185352772

Reorder the terms:
7 + a = -8.185352772

Solving
7 + a = -8.185352772

Solving for variable 'a'.

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

Add '-7' to each side of the equation.
7 + -7 + a = -8.185352772 + -7

Combine like terms: 7 + -7 = 0
0 + a = -8.185352772 + -7
a = -8.185352772 + -7

Combine like terms: -8.185352772 + -7 = -15.185352772
a = -15.185352772

Simplifying
a = -15.185352772


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.185352772, -15.185352772}

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