a^2+14a-49=0

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Solution for a^2+14a-49=0 equation: 


Simplifying
a2 + 14a + -49 = 0

Reorder the terms:
-49 + 14a + a2 = 0

Solving
-49 + 14a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 14a + 49 + a2 = 0 + 49

Reorder the terms:
-49 + 49 + 14a + a2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 14a + a2 = 0 + 49
14a + a2 = 0 + 49

Combine like terms: 0 + 49 = 49
14a + a2 = 49

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 = 49 + 49

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

Combine like terms: 49 + 49 = 98
49 + 14a + a2 = 98

Factor a perfect square on the left side:
(a + 7)(a + 7) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(a + 7) equal to 9.899494937 and -9.899494937.


Subproblem 1
a + 7 = 9.899494937

Simplifying
a + 7 = 9.899494937

Reorder the terms:
7 + a = 9.899494937

Solving
7 + a = 9.899494937

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 = 9.899494937 + -7

Combine like terms: 7 + -7 = 0
0 + a = 9.899494937 + -7
a = 9.899494937 + -7

Combine like terms: 9.899494937 + -7 = 2.899494937
a = 2.899494937

Simplifying
a = 2.899494937


Subproblem 2
a + 7 = -9.899494937

Simplifying
a + 7 = -9.899494937

Reorder the terms:
7 + a = -9.899494937

Solving
7 + a = -9.899494937

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 = -9.899494937 + -7

Combine like terms: 7 + -7 = 0
0 + a = -9.899494937 + -7
a = -9.899494937 + -7

Combine like terms: -9.899494937 + -7 = -16.899494937
a = -16.899494937

Simplifying
a = -16.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.899494937, -16.899494937}

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